do x rays travel at the speed of sound

Electromagnetic Radiation

Claimed by Zoila de Leon (Fall 2023)

1.1 What is a Electromagnetic(EM) Radiation?
1.2 General Properties
1.3 Problem Solving Method and Equations
1.4 Fields Made by Charges and Fields Made by Monopoles
2 The EM Spectrum
3 Waves and Fields
4 A Mathematical Model
5 Connectedness: X-Rays
6.1 Practice Problems (new section by Zoila)
7 References

What is a Electromagnetic(EM) Radiation?

Electromagnetic radiation is a form of energy that is all around us and takes many forms, such as radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma rays.

Before 1873, electricity and magnetism were thought to be two different forces. However, in 1873, Scottish Physicist James Maxwell developed his famous theory of electromagnetism. There are four main electro magnetic interactions according to Maxwell:

The force of attraction or repulsion between electric charges is inversely proportional to the square of the distance between them
Magnetic poles come in pairs that attract and repel each other much as electric charges do
An electric current in a wire produces a magnetic field whose direction depends on the direction of the current
A moving electric field produces a magnetic field, and vice versa

General Properties

The four Maxwell's Equations provide a complete description of possible spatial patterns of electric and magnetic field in space.

The Ampere-Maxwell Law
Gauss's Law
Faraday's Law

Other than Maxwell's Four equations, there are general properties of all electromagnetic radiation:

Electromagnetic radiation can travel through empty space. Most other types of waves must travel through some sort of substance. For example, sound waves need either a gas, solid, or liquid to pass through in order to be heard
The speed of light is always a constant (3 x 10^8 m/s)
Wavelengths are measured between the distances of either crests or troughs. It is usually characterized by the Greek symbol λ (lambda).

Electromagnetic waves are the self-propagating, mutual oscillation of electric and magnetic fields. The propagation of electromagnetic energy is often referred to as radiation. We can also say that the 'pulse' of these moving fields result in radiation (7).

The equation for propagation is E=cB with c being the speed of light. This equation is derived from combining the two equations E=vB and B=u0e0vE, proving that v is equal to 3e8 meters/second.

Problem Solving Method and Equations

To go about solving/analyzing mathematically an electromagnetic field using Maxwell's equations,this is how we proceed (7)

Establish the space and time in which the electric and magnetic fields are present
Check that Maxwell's equations can be applied in the situation above
Check when the charge accelerates, it produces these fields and therefore radiation
Show how these fields would interact with matter

The equation of the Radiative Electric Field is: E= 1/(4πe0)*-qa/(c^2r) where a is the acceleration of the particle, c is the speed of light and r is the distance from the original location of the charge to right before the kink. This kink happens on the electric field because of the slight delay when the charge is moved.

Fields Made by Charges and Fields Made by Monopoles

We can differentiate fields made by charges and the ones made by magnetic monopoles. (7) For fields made by charges, when the charge is

at rest, E=1/r^2 and B=0
constant speed, E=1/r^2 and B=1/r^2
accelerating, E=1/r and B=1/r

For fields made by magnetic monopoles, the first point would have E and B switched.

The EM Spectrum

EM spectrum is a span of enormous range of wavelengths and frequencies. The EM spectrum is generally divided into 7 different regions, in order of decreasing wavelength and increasing energy and frequency. It ranges from Gamma rays to Long Radio Waves. Following are the lists of waves:

Visible Light
Infrared Rays
Long radio waves

Although all these waves do different things, there is one thing in common : They all travel in waves.

Infrared radiation can be released as heat or thermal energy. It can also be bounced back, which is called near infrared because of its similarities with visible light energy. Infrared Radiation is most commonly used in remote sensing as infrared sensors collect thermal energy, providing us with weather conditions.

Visible Light is the only part of the electromagnetic spectrum that humans can see with a naked eye. This part of the spectrum includes a range of different colors that all represent a particular wavelength. Rainbows are formed in this way; light passes through matter in which it is absorbed or reflected based on its wavelength. As a result, some colors are reflected more than other, leading to the creation of a rainbow.

Waves and Fields

As we learned in class, electric field is produced when an electron is accelerating. Likewise, EM radiation is created when an atomic particle, like an electron, is accelerated by an electric field. The movement like this produces oscillating electric and magnetic fields, which travel at right angles to each other in a bundle of light energy called a photon. Photons travel in a harmonic wave at the fastest speed possible in the universe.

Electromagnetic waves are formed when an electric field couples with a magnetic field. Magnetic and electric fields of an electromagnetic wave are perpendicular to each other and to the direction of the wave.

A wavelength (in m) is the distance between two consecutive peaks of a wave. Frequency is the number of waves that form in a given length of time. A wavelength and frequency are interrelated. A short wavelength indicates that the frequency will be higher because one cycle can pass in a shorter amount of time. Likewise, a longer wavelength has a lower frequency because each cycle takes longer to complete.

Waves can be classified according to their nature:

Mechanical waves
Electromagnetic waves

Mechanical Waves

Mechanical waves require a medium (matter) to travel through. Examples are sound waves, water waves, ripples in strings or springs.

Water Waves

Sound Waves

Electromagnetic Waves

Electromagnetic waves do not require a medium (matter) to travel through - they can travel through space. Examples are radio waves, visible light, x-rays.

Radio Waves

Visible Lights

A Mathematical Model

The position of the particle is defined by a sine wave:

y = ymaxsin(wt)

Where w is the angular frequency

Amplitude is the distance from the maximum vertical displacement of the wave to the middle of the wave. The Amplitude of the sinusoidal Wave is the height of the peak in the wave measured from the zero line. This measures the magnitude of oscillation of a particular wave. The Amplitude is important because it tells you the intensity or brightness of a wave in comparison with other waves.

The period of the wave is the time between crests in seconds(s).

T = 2pi/w-----(units of seconds)

Frequency is the number of cycles per second, and is expressed as sec-1 or Hertz(Hz). Frequency is directly proportional to energy and can be express as "

E = hv where E is energy, h is Planck's constant ( 6.62607*10^-34J) and v is frequency

f = 1/T f = w/2pi----(Units Hertz)

Wavelength is the distance between crests in meters. Wavelength is equal to the speed of light times frequency. Longer wavelength waves such as radio waves carry low energy; this is why we can listen to the radio without any harmful consequences. Shorter wavelength waves such as x-rays carry higher energy that can be hazardous to our health.

Wavelength and Frequency

The speed of light is the multiplication of the wavelength and frequency.

This diagram shows all properties of waves:

ENERGY FLUX

Is defined by the following equation:

Connectedness: X-Rays

Electromagnetic Radiation while commonly thought of as only including visible light, radio waves, UV waves, and gamma rays; also include X-rays. In 1895, X-rays were initially discovered by William Roentgen, who accidentally fell upon the most important discovery about his life (Figure 1). Roentgen was already working on cathode rays, and because of a fluorescent glow that occurred during his experiments, covered his experimental apparatus with heavy black paper. However, when he did this, he discovered a glow coming from a screen several feet away. Through many more experiments, he discovered that a new type of energy, not cathode rays, were the cause of the glow. He named them “x-rays” and received the 1901 Nobel Prize in Physics. Roentgen never patented his monumental discovery and as a result, numerous researchers set out to find a multitude of uses and capitalize on his work.

Primarily, people could now view objects that were hidden from plain view (i.e. scanners in airports). While X-rays are now used in 100’s of professions (security, chemistry, art galleries), its most important function is to view bones to determine abnormalities in humans. In fact, one of Roentgen’s first x-rays was of his wife’s hand (Figure 2). X-rays fall under the scope of electromagnetic radiation because, like all E.R. waves, it is comprised of photons. X-rays have wavelengths between 0.01 to 10 nanometers and fall between UV and Gamma Waves on the E.R. spectrum (Figure 3). There are two main methods in which an x-ray may be formed. Both require a vacuum-filled tube called an x-ray tube (Figure 4). With an anode on one end and a cathode on the other, an electric current is applied and a high energy electron is projected from the cathode, through the vacuum, and at the anode. In the characteristic x-ray generation approach, the electron from the cathode collides with an inner shell electron on an atom on the anode (Figure 5). Both of these electrons are ejected from the atom and an outer shell electron takes the place of the inner shell one. Because the outer electron must have a lower energy to fill the inner shell hole, it releases a photon with the equivalent energy of the difference between the two energy levels in the atom. This photon is the x-ray that is used to view objects such as bones.

In the Bremsstrahlung x-ray generation method, the electron from the cathode is slowed as it passes the nucleus of an atom at the anode (Figure 6). As it slows and its path is changed, the loses energy (kinetic energy). This energy is also released as a photon which is subsequently called an x-ray. Depending on the voltage and current of the tube and the material of the anode, different types (as in wavelengths and energy) of x-rays can be produced and each one. However, all X-rays will continue to pass through objects until it reaches a material dense that stops it. However, density of the material required depends on the energy of the x-ray. For example, during a medical x-ray, x-rays of a certain energy will pass through soft tissue (skin, organs, etc) but not through bones. The x-rays that pass through the soft tissue will strike the screen and the absence of the x-rays absorbed by the bones will cause a negative space on the screen. The areas where x-rays do not strike will form the image of the bone. While the principles remain the same, x-ray machines today use incredible sophisticated technology to specify the type of x-ray they want and have greatly increased in accuracy since Roentgen’s initial discovery.

Information and photographs are pulled from references 1 through 5 cited below*

Already, during the Ancient Greek and Roman times, light was studied as the presence of deflection and refraction were noticed. Electromagnetic radiation of wavelengths in the early 19th century. The discovery of infrared radiation is ascribed to astronomer William Herschel, who published his results in 1800 before the Royal Society of London. Herschel used a glass Triangular prism (optics)|prism to refract light from the Sun and detected invisible rays that caused heating beyond the red part of the spectrum, through an increase in the temperature recorded with a thermometer. These "calorific rays" were later termed infrared.

In 1801, Rohann Ritter, discovered the presence of ultraviolet light using salts. It was known that light could darken some silver halides and while doing so, he realized that the region beyond the violet bar (therefore ultraviolet) was more effective in changing the color of the halides. However,in 1864, while summarizing the theories of his time accumulating into his famous set of Maxwell equations, James Clerk Maxwell managed to deduce the speed of light being around 3e8 meters per second. This was instrumental in creating the rest of the spectrum.

In 1887-1888 Physicist Heinrich Hertz not only tried to measure the velocity and frequency of electromagnetic radiation waves at other parts of the known spectrum of the time, but he was also able to prove that Maxwell's findings were correct. He did this on the microwave radiation as well.

The discovery of X-rays occurred in 1895 by Wilhelm Rontgen when his barium platinocyanide detector screen began to glow under the presence of a discharge that passed through a cathode ray tube although the latter was completely covered. Once he determined its possible use, he tried to look at his wife's hand using this new discovery. However x-ray spectroscopy was not institutionalized until later by Karl Manne Siegbahn.

In 1900, Paul Villard discovered Gamma rays although he initially thought that they were particles similar to alpha and beta particles which were emitted during radiation. These 'particles' were later proven to be part of the electromagnetic spectrum.

Practice Problems (new section by Zoila)

1. Elert, Glenn. "X-rays." X-rays – The Physics Hypertextbook. N.p., n.d. Web. 08 Apr. 2017. http://physics.info/x-ray/

2."X-rays." X-rays. N.p., n.d. Web. 08 Apr. 2017. http://www.physics.isu.edu/radinf/xray.htm

3. "Basics of X-ray PhysicsX-ray production." Welcome to Radiology Masterclass. N.p., n.d. Web. 08 Apr. 2017. http://www.radiologymasterclass.co.uk/tutorials/physics/x-ray_physics_production#top_2nd_img

4. "X-Rays." Image: Electromagnetic Spectrum. N.p., n.d. Web. 08 Apr. 2017. https://www.boundless.com/physics/textbooks/boundless-physics-textbook/electromagnetic-waves-23/the-electromagnetic-spectrum-165/x-rays-597-11175/images/electromagnetic-spectrum/

5. "This Month in Physics History." American Physical Society. N.p., n.d. Web. 08 Apr. 2017. https://www.aps.org/publications/apsnews/200111/history.cfm

6. Editors, Spectroscopy. “The Electromagnetic Spectrum: A History.” Spectroscopy Home, 27 Oct. 2017, www.spectroscopyonline.com/electromagnetic-spectrum-history?id=&sk=&date=&&pageID=4.

7. Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interaction II: Electric & Magnetic Interactions, Version 1.2. John Wiley & Sons, 2003.

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Speed of Sound in Physics

In physics, the speed of sound is the distance traveled per unit of time by a sound wave through a medium. It is highest for stiff solids and lowest for gases. There is no sound or speed of sound in a vacuum because sound (unlike light ) requires a medium in order to propogate.

What Is the Speed of Sound?

Usually, conversations about the speed of sound refer to the speed of sound of dry air (humidity changes the value). The value depends on temperature.

at 20 ° C or 68 ° F: 343 m/s or 1234.8 kph or 1125ft/s or 767 mph
at 0 ° C or 32 ° F: 331 m/s or 1191.6 kph or 1086 ft/s or 740 mph

Mach Numher

The Mach number is the ratio of air speed to the speed of sound. So, an object at Mach 1 is traveling at the speed of sound. Exceeding Mach 1 is breaking the sound barrier or is supersonic . At Mach 2, the object travels twice the speed of sound. Mach 3 is three times the speed of sound, and so on.

Remember that the speed of sound depends on temperature, so you break sound barrier at a lower speed when the temperature is colder. To put it another way, it gets colder as you get higher in the atmosphere, so an aircraft might break the sound barrier at a higher altitude even if it does not increase its speed.

Solids, Liquids, and Gases

The speed of sound is greatest for solids, intermediate for liquids, and lowest for gases:

v solid > v liquid >v gas

Particles in a gas undergo elastic collisions and the particles are widely separated. In contrast, particles in a solid are locked into place (rigid or stiff), so a vibration readily transmits through chemical bonds.

Here are examples of the difference between the speed of sound in different materials:

Diamond (solid): 12000 m/s
Copper (solid): 6420 m/s
Iron (solid): 5120 m/s
Water (liquid) 1481 m/s
Helium (gas): 965 m/s
Dry air (gas): 343 m/s

Sounds waves transfer energy to matter via a compression wave (in all phases) and also shear wave (in solids). The pressure disturbs a particle, which then impacts its neighbor, and continues traveling through the medium. The speed is how quickly the wave moves, while the frequency is the number of vibrations the particle makes per unit of time.

The Hot Chocolate Effect

The hot chocolate effect describes the phenomenon where the pitch you hear from tapping a cup of hot liquid rises after adding a soluble powder (like cocoa powder into hot water). Stirring in the powder introduces gas bubbles that reduce the speed of sound of the liquid and lower the frequency (pitch) of the waves. Once the bubbles clear, the speed of sound and the frequency increase again.

Speed of Sound Formulas

There are several formulas for calculating the speed of sound. Here are a few of the most common ones:

For gases these approximations work in most situations:

For this formula, use the Celsius temperature of the gas.

v = 331 m/s + (0.6 m/s/C)•T

Here is another common formula:

v = (γRT) 1/2

γ is the ratio of specific heat values or adiabatic index (1.4 for air at STP )
R is a gas constant (282 m 2 /s 2 /K for air)
T is the absolute temperature (Kelvin)

The Newton-Laplace formula works for both gases and liquids (fluids):

v = (K s /ρ) 1/2

K s is the coefficient of stiffness or bulk modulus of elasticity for gases
ρ is the density of the material

So solids, the situation is more complicated because shear waves play into the formula. There can be sound waves with different velocities, depending on the mode of deformation. The simplest formula is for one-dimensional solids, like a long rod of a material:

v = (E/ρ) 1/2

E is Young’s modulus

Note that the speed of sound decreases with density! It increases according to the stiffness of a medium. This is not intuitively obvious, since often a dense material is also stiff. But, consider that the speed of sound in a diamond is much faster than the speed in iron. Diamond is less dense than iron and also stiffer.

Factors That Affect the Speed of Sound

The primary factors affecting the speed of sound of a fluid (gas or liquid) are its temperature and its chemical composition. There is a weak dependence on frequency and atmospheric pressure that is omitted from the simplest equations.

While sound travels only as compression waves in a fluid, it also travels as shear waves in a solid. So, a solid’s stiffness, density, and compressibility also factor into the speed of sound.

Speed of Sound on Mars

Thanks to the Perseverance rover, scientists know the speed of sound on Mars. The Martian atmosphere is much colder than Earth’s, its thin atmosphere has a much lower pressure, and it consists mainly of carbon dioxide rather than nitrogen. As expected, the speed of sound on Mars is slower than on Earth. It travels at around 240 m/s or about 30% slower than on Earth.

What scientists did not expect is that the speed of sound varies for different frequencies. A high pitched sound, like from the rover’s laser, travels faster at around 250 m/s. So, for example, if you listened to a symphony recording from a distance on Mars you’d hear the various instruments at different times. The explanation has to do with the vibrational modes of carbon dioxide, the primary component of the Martian atmosphere. Also, it’s worth noting that the atmospheric pressure is so low that there really isn’t any much sound at all from a source more than a few meters away.

Speed of Sound Example Problems

Find the speed of sound on a cold day when the temperature is 2 ° C.

The simplest formula for finding the answer is the approximation:

v = 331 m/s + (0.6 m/s/C) • T

Since the given temperature is already in Celsius, just plug in the value:

v = 331 m/s + (0.6 m/s/C) • 2 C = 331 m/s + 1.2 m/s = 332.2 m/s

You’re hiking in a canyon, yell “hello”, and hear an echo after 1.22 seconds. The air temperature is 20 ° C. How far away is the canyon wall?

The first step is finding the speed of sound at the temperature:

v = 331 m/s + (0.6 m/s/C) • T v = 331 m/s + (0.6 m/s/C) • 20 C = 343 m/s (which you might have memorized as the usual speed of sound)

Next, find the distance using the formula:

d = v• T d = 343 m/s • 1.22 s = 418.46 m

But, this is the round-trip distance! The distance to the canyon wall is half of this or 209 meters.

If you double the frequency of sound, it double the speed of its waves. True or false?

This is (mostly) false. Doubling the frequency halves the wavelength, but the speed depends on the properties of the medium and not its frequency or wavelength. Frequency only affects the speed of sound for certain media (like the carbon dioxide atmosphere of Mars).

Everest, F. (2001). The Master Handbook of Acoustics . New York: McGraw-Hill. ISBN 978-0-07-136097-5.
Kinsler, L.E.; Frey, A.R.; Coppens, A.B.; Sanders, J.V. (2000). Fundamentals of Acoustics (4th ed.). New York: John Wiley & Sons. ISBN 0-471-84789-5.
Maurice, S.; et al. (2022). “In situ recording of Mars soundscape:. Nature. 605: 653-658. doi: 10.1038/s41586-022-04679-0
Wong, George S. K.; Zhu, Shi-ming (1995). “Speed of sound in seawater as a function of salinity, temperature, and pressure”. The Journal of the Acoustical Society of America . 97 (3): 1732. doi: 10.1121/1.413048

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Physics library

Course: physics library > unit 14, light: electromagnetic waves, the electromagnetic spectrum and photons.

Electromagnetic waves and the electromagnetic spectrum
Polarization of light, linear and circular

Introduction to electromagnetic waves

Basic properties of waves: amplitude, wavelength, and frequency, example: calculating the wavelength of a light wave, the electromagnetic spectrum, quantization of energy and the dual nature of light, example: calculating the energy of a photon, attributions.

“ Electromagnetic Radiation ” from UC Davis ChemWiki, CC BY-NC-SA 3.0

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Since the speed of a wave is defined as the distance that a point on a wave (such as a compression or a rarefaction) travels per unit of time, it is often expressed in units of meters/second (abbreviated m/s). In equation form, this is

The faster a sound wave travels, the more distance it will cover in the same period of time. If a sound wave were observed to travel a distance of 700 meters in 2 seconds, then the speed of the wave would be 350 m/s. A slower wave would cover less distance - perhaps 660 meters - in the same time period of 2 seconds and thus have a speed of 330 m/s. Faster waves cover more distance in the same period of time.

Factors Affecting Wave Speed

The speed of any wave depends upon the properties of the medium through which the wave is traveling. Typically there are two essential types of properties that affect wave speed - inertial properties and elastic properties. Elastic properties are those properties related to the tendency of a material to maintain its shape and not deform whenever a force or stress is applied to it. A material such as steel will experience a very small deformation of shape (and dimension) when a stress is applied to it. Steel is a rigid material with a high elasticity. On the other hand, a material such as a rubber band is highly flexible; when a force is applied to stretch the rubber band, it deforms or changes its shape readily. A small stress on the rubber band causes a large deformation. Steel is considered to be a stiff or rigid material, whereas a rubber band is considered a flexible material. At the particle level, a stiff or rigid material is characterized by atoms and/or molecules with strong attractions for each other. When a force is applied in an attempt to stretch or deform the material, its strong particle interactions prevent this deformation and help the material maintain its shape. Rigid materials such as steel are considered to have a high elasticity. (Elastic modulus is the technical term). The phase of matter has a tremendous impact upon the elastic properties of the medium. In general, solids have the strongest interactions between particles, followed by liquids and then gases. For this reason, longitudinal sound waves travel faster in solids than they do in liquids than they do in gases. Even though the inertial factor may favor gases, the elastic factor has a greater influence on the speed ( v ) of a wave, thus yielding this general pattern:

Inertial properties are those properties related to the material's tendency to be sluggish to changes in its state of motion. The density of a medium is an example of an inertial property . The greater the inertia (i.e., mass density) of individual particles of the medium, the less responsive they will be to the interactions between neighboring particles and the slower that the wave will be. As stated above, sound waves travel faster in solids than they do in liquids than they do in gases. However, within a single phase of matter, the inertial property of density tends to be the property that has a greatest impact upon the speed of sound. A sound wave will travel faster in a less dense material than a more dense material. Thus, a sound wave will travel nearly three times faster in Helium than it will in air. This is mostly due to the lower mass of Helium particles as compared to air particles.

The Speed of Sound in Air

The speed of a sound wave in air depends upon the properties of the air, mostly the temperature, and to a lesser degree, the humidity. Humidity is the result of water vapor being present in air. Like any liquid, water has a tendency to evaporate. As it does, particles of gaseous water become mixed in the air. This additional matter will affect the mass density of the air (an inertial property). The temperature will affect the strength of the particle interactions (an elastic property). At normal atmospheric pressure, the temperature dependence of the speed of a sound wave through dry air is approximated by the following equation:

where T is the temperature of the air in degrees Celsius. Using this equation to determine the speed of a sound wave in air at a temperature of 20 degrees Celsius yields the following solution.

v = 331 m/s + (0.6 m/s/C)•(20 C)

v = 331 m/s + 12 m/s

v = 343 m/s

(The above equation relating the speed of a sound wave in air to the temperature provides reasonably accurate speed values for temperatures between 0 and 100 Celsius. The equation itself does not have any theoretical basis; it is simply the result of inspecting temperature-speed data for this temperature range. Other equations do exist that are based upon theoretical reasoning and provide accurate data for all temperatures. Nonetheless, the equation above will be sufficient for our use as introductory Physics students.)

Look It Up!

Using wave speed to determine distances.

At normal atmospheric pressure and a temperature of 20 degrees Celsius, a sound wave will travel at approximately 343 m/s; this is approximately equal to 750 miles/hour. While this speed may seem fast by human standards (the fastest humans can sprint at approximately 11 m/s and highway speeds are approximately 30 m/s), the speed of a sound wave is slow in comparison to the speed of a light wave. Light travels through air at a speed of approximately 300 000 000 m/s; this is nearly 900 000 times the speed of sound. For this reason, humans can observe a detectable time delay between the thunder and the lightning during a storm. The arrival of the light wave from the location of the lightning strike occurs in so little time that it is essentially negligible. Yet the arrival of the sound wave from the location of the lightning strike occurs much later. The time delay between the arrival of the light wave (lightning) and the arrival of the sound wave (thunder) allows a person to approximate his/her distance from the storm location. For instance if the thunder is heard 3 seconds after the lightning is seen, then sound (whose speed is approximated as 345 m/s) has traveled a distance of

If this value is converted to miles (divide by 1600 m/1 mi), then the storm is a distance of 0.65 miles away.

Another phenomenon related to the perception of time delays between two events is an echo . A person can often perceive a time delay between the production of a sound and the arrival of a reflection of that sound off a distant barrier. If you have ever made a holler within a canyon, perhaps you have heard an echo of your holler off a distant canyon wall. The time delay between the holler and the echo corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back. A measurement of this time would allow a person to estimate the one-way distance to the canyon wall. For instance if an echo is heard 1.40 seconds after making the holler , then the distance to the canyon wall can be found as follows:

The canyon wall is 242 meters away. You might have noticed that the time of 0.70 seconds is used in the equation. Since the time delay corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back, the one-way distance to the canyon wall corresponds to one-half the time delay.

While an echo is of relatively minimal importance to humans, echolocation is an essential trick of the trade for bats. Being a nocturnal creature, bats must use sound waves to navigate and hunt. They produce short bursts of ultrasonic sound waves that reflect off objects in their surroundings and return. Their detection of the time delay between the sending and receiving of the pulses allows a bat to approximate the distance to surrounding objects. Some bats, known as Doppler bats, are capable of detecting the speed and direction of any moving objects by monitoring the changes in frequency of the reflected pulses. These bats are utilizing the physics of the Doppler effect discussed in an earlier unit (and also to be discussed later in Lesson 3 ). This method of echolocation enables a bat to navigate and to hunt.

The Wave Equation Revisited

Like any wave, a sound wave has a speed that is mathematically related to the frequency and the wavelength of the wave. As discussed in a previous unit , the mathematical relationship between speed, frequency and wavelength is given by the following equation.

Using the symbols v , λ , and f , the equation can be rewritten as

Check Your Understanding

1. An automatic focus camera is able to focus on objects by use of an ultrasonic sound wave. The camera sends out sound waves that reflect off distant objects and return to the camera. A sensor detects the time it takes for the waves to return and then determines the distance an object is from the camera. If a sound wave (speed = 340 m/s) returns to the camera 0.150 seconds after leaving the camera, how far away is the object?

Answer = 25.5 m

The speed of the sound wave is 340 m/s. The distance can be found using d = v • t resulting in an answer of 25.5 m. Use 0.075 seconds for the time since 0.150 seconds refers to the round-trip distance.

2. On a hot summer day, a pesky little mosquito produced its warning sound near your ear. The sound is produced by the beating of its wings at a rate of about 600 wing beats per second.

a. What is the frequency in Hertz of the sound wave? b. Assuming the sound wave moves with a velocity of 350 m/s, what is the wavelength of the wave?

Part a Answer: 600 Hz (given)

Part b Answer: 0.583 meters

3. Doubling the frequency of a wave source doubles the speed of the waves.

a. True b. False

Doubling the frequency will halve the wavelength; speed is unaffected by the alteration in the frequency. The speed of a wave depends upon the properties of the medium.

4. Playing middle C on the piano keyboard produces a sound with a frequency of 256 Hz. Assuming the speed of sound in air is 345 m/s, determine the wavelength of the sound corresponding to the note of middle C.

Answer: 1.35 meters (rounded)

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 256 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

5. Most people can detect frequencies as high as 20 000 Hz. Assuming the speed of sound in air is 345 m/s, determine the wavelength of the sound corresponding to this upper range of audible hearing.

Answer: 0.0173 meters (rounded)

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 20 000 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

6. An elephant produces a 10 Hz sound wave. Assuming the speed of sound in air is 345 m/s, determine the wavelength of this infrasonic sound wave.

Answer: 34.5 meters

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 10 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

7. Determine the speed of sound on a cold winter day (T=3 degrees C).

Answer: 332.8 m/s

The speed of sound in air is dependent upon the temperature of air. The dependence is expressed by the equation:

v = 331 m/s + (0.6 m/s/C) • T

where T is the temperature in Celsius. Substitute and solve.

v = 331 m/s + (0.6 m/s/C) • 3 C v = 331 m/s + 1.8 m/s v = 332.8 m/s

8. Miles Tugo is camping in Glacier National Park. In the midst of a glacier canyon, he makes a loud holler. He hears an echo 1.22 seconds later. The air temperature is 20 degrees C. How far away are the canyon walls?

Answer = 209 m

The speed of the sound wave at this temperature is 343 m/s (using the equation described in the Tutorial). The distance can be found using d = v • t resulting in an answer of 343 m. Use 0.61 second for the time since 1.22 seconds refers to the round-trip distance.

9. Two sound waves are traveling through a container of unknown gas. Wave A has a wavelength of 1.2 m. Wave B has a wavelength of 3.6 m. The velocity of wave B must be __________ the velocity of wave A.

a. one-ninth b. one-third c. the same as d. three times larger than

The speed of a wave does not depend upon its wavelength, but rather upon the properties of the medium. The medium has not changed, so neither has the speed.

10. Two sound waves are traveling through a container of unknown gas. Wave A has a wavelength of 1.2 m. Wave B has a wavelength of 3.6 m. The frequency of wave B must be __________ the frequency of wave A.

Since Wave B has three times the wavelength of Wave A, it must have one-third the frequency. Frequency and wavelength are inversely related.

Interference and Beats

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Chapter 2.1: Waves and Electromagnetic Radiation

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Learning Objectives

To learn about the characteristics of electromagnetic waves.
Types include light, X-Rays, infrared and microwaves.

Scientists discovered much of what we know about the structure of the atom by observing the interaction of atoms with various forms of radiant, or transmitted, energy, such as the energy associated with the visible light we detect with our eyes, the infrared radiation we feel as heat, the ultraviolet light that causes sunburn, and the x-rays that produce images of our teeth or bones. All these forms of radiant energy should be familiar to you. We begin our discussion of the development of our current atomic model by describing the properties of waves and the various forms of electromagnetic radiation.

Figure 2.1.1 A Wave in Water

When a drop of water falls onto a smooth water surface, it generates a set of waves that travel outward in a circular direction.

Properties of Waves

A wave A periodic oscillation that transmits energy through space. is a periodic oscillation that transmits energy through space. Anyone who has visited a beach or dropped a stone into a puddle has observed waves traveling through water ( Figure 2.1.1 ). These waves are produced when wind, a stone, or some other disturbance, such as a passing boat, transfers energy to the water, causing the surface to oscillate up and down as the energy travels outward from its point of origin. As a wave passes a particular point on the surface of the water, anything floating there moves up and down.

Figure 2.1.2 Important Properties of Waves

The wavelength is the distance from one peak to the next peak. The amplitude is the height of the peak.

(a) Wavelength (λ in meters), frequency (ν, in Hz), and amplitude are indicated on this drawing of a wave. (b) The wave with the shortest wavelength has the greatest number of wavelengths per unit time (i.e., the highest frequency). If two waves have the same frequency and speed, the one with the greater amplitude has the higher energy.

Waves have characteristic properties ( Figure 2.1.2 ). As you may have noticed in Figure 2.1.1 , waves are periodic Phenomena , such as waves, that repeat regularly in both space and time. ; that is, they repeat regularly in both space and time. The distance between two corresponding points in a wave—between the midpoints of two peaks, for example, or two troughs—is the wavelength (λ) The distance between two corresponding points in a wave—between the midpoints of two peaks or two troughs. . λ is the lowercase Greek lambda, and ν is the lowercase Greek nu. Wavelengths are described by a unit of distance, typically meters. The frequency (ν) The number of oscillations (i.e., of a wave) that pass a particular point in a given period of time. of a wave is the number of oscillations that pass a particular point in a given period of time. The usual units are oscillations per second (1/s = s −1 ), which in the SI system is called the hertz (Hz). It is named after German physicist Heinrich Hertz (1857–1894), a pioneer in the field of electromagnetic radiation. The amplitude The vertical height of a wave, which is defined as half the peak-to-trough height. , or vertical height, of a wave is defined as half the peak-to-trough height; as the amplitude of a wave with a given frequency increases, so does its energy. As you can see in Figure 2.1.2 , two waves can have the same amplitude but different wavelengths and vice versa. The distance traveled by a wave per unit time is its speed ( v ) The distance traveled by a wave per unit time. , which is typically measured in meters per second (m/s). The speed of a wave is equal to the product of its wavelength and frequency:

\( (wavelength)(frequency) = speed \tag{2.1.1} \)

\( \lambda \nu =v \)

\( \left ( \frac{meters}{\cancel{wave}} \right )\left ( \frac{\cancel{wave}}{second} \right )=\frac{meters}{second} \)

Be careful not to confuse the symbols for the speed, v , with the frequency, ν.

Water waves are slow compared to sound waves, which can travel through solids, liquids, and gases. Whereas water waves may travel a few meters per second, the speed of sound in dry air at 20°C is 343.5 m/s. Ultrasonic waves, which travel at an even higher speed (>1500 m/s) and have a greater frequency, are used in such diverse applications as locating underwater objects and the medical imaging of internal organs.

Light Speed, Wavelength, and Frequency | Dimensional Analysis by Doc Schuster

Waves in General by JaHu Productions - a bit faster. Also discusses sound waves

Electromagnetic Radiation

Figure 2.1.3 The Nature of Electromagnetic Radiation

Diagram showing the oscillations of electric field on the x-axis and magnetic field on the y-axis moving in a direction from the source.

Figure 2.1.3 The Nature of Electromagnetic Radiation All forms of electromagnetic radiation consist of perpendicular oscillating electric and magnetic fields.

Water waves transmit energy through space by the periodic oscillation of matter (the water). In contrast, energy that is transmitted, or radiated, through space in the form of periodic oscillations of electric and magnetic fields is known as electromagnetic radiation Energy that is transmitted, or radiated, through space in the form of periodic oscillations of electric and magnetic fields. ( Figure 2.1.3 ). Some forms of electromagnetic radiation are shown in Figure 2.1.4 . In a vacuum, all forms of electromagnetic radiation—whether microwaves, visible light, or gamma rays—travel at the speed of light ( c ) The speed with which all forms of electromagnetic radiation travel in a vacuum. , a fundamental physical constant with a value of 2.99792458 × 10 8 m/s (which is about 3.00 ×10 8 m/s or 1.86 × 10 5 mi/s). This is about a million times faster than the speed of sound.

Because the various kinds of electromagnetic radiation all have the same speed ( c ), they differ in only wavelength and frequency. As shown in Figure 2.1.4 and Table 2.1.1 , the wavelengths of familiar electromagnetic radiation range from 10 1 m for radio waves to 10 −12 m for gamma rays, which are emitted by nuclear reactions. By replacing v with c in Equation 2.1.1 , we can show that the frequency of electromagnetic radiation is inversely proportional to its wavelength:

\( \begin{array}{cc} c=\lambda \nu \\ \nu =\dfrac{c}{\lambda } \end{array} \tag{2.1.2} \)

For example, the frequency of radio waves is about 10 8 Hz, whereas the frequency of gamma rays is about 10 20 Hz. Visible light, which is electromagnetic radiation that can be detected by the human eye, has wavelengths between about 7 × 10 −7 m (700 nm, or 4.3 × 10 14 Hz) and 4 × 10 −7 m (400 nm, or 7.5 × 10 14 Hz). Note that when frequency increases, wavelength decreases; c being a constant stays the same. Similarly when frequency decreases, wavelength increases,

Here is a video from Oxford University Press which goes through the calculation

Calculating Frequency Given Wavelength - Johnny Cantrell
. Wavelength Frequency Problems - Cayer Chem
Q uantum Chemistry - Ohio State
Quantum Chemistry Quizzes - mhe education
AP Chemistry Chapter 7 Review - Science Geek
Quantum Theory of the Atom Practice Quiz - Northrup

Answers for these quizzes are included. There are also questions covering more topics in Chapter 2.

Within this visible range our eyes perceive radiation of different wavelengths (or frequencies) as light of different colors, ranging from red to violet in order of decreasing wavelength. The components of white light—a mixture of all the frequencies of visible light—can be separated by a prism, as shown in part (b) in Figure 2.1.4 . A similar phenomenon creates a rainbow, where water droplets suspended in the air act as tiny prisms.

Figure 2.1.4 The Electromagnetic Spectrum (a) This diagram shows the wavelength and frequency ranges of electromagnetic radiation. The visible portion of the electromagnetic spectrum is the narrow region with wavelengths between about 400 and 700 nm. (b) When white light is passed through a prism, it is split into light of different wavelengths, whose colors correspond to the visible spectrum.

This video reviews the ideas in Figure 2.1.4

Table 2.1.1 Common Wavelength Units for Electromagnetic Radiation

As you will soon see, the energy of electromagnetic radiation is directly proportional to its frequency and inversely proportional to its wavelength:

\( E\; \propto\; \nu \tag{2.1.3} \)

\( E\; \propto\; \dfrac{1}{\lambda } \tag{2.1.4}\)

Note the Pattern

The energy of electromagnetic radiation increases with increasing frequency and decreasing wavelength.

Example 2.1.1

Your favorite FM radio station, WXYZ, broadcasts at a frequency of 101.1 MHz. What is the wavelength of this radiation?

Given: frequency

Asked for: wavelength

Substitute the value for the speed of light in meters per second into Equation 2.1.2 to calculate the wavelength in meters.

From Equation 2.1.2 , we know that the product of the wavelength and the frequency is the speed of the wave, which for electromagnetic radiation is 2.998 × 10 8 m/s:

\( \lambda \nu = c = 2.998 \times 10^{8} m/s \)

Thus the wavelength λ is given by

\( \lambda =\dfrac{c}{\nu }=\left ( \dfrac{2.988\times 10^{8}\; m/\cancel{s}}{101.1\; \cancel{MHz}} \right )\left ( \dfrac{1\; \cancel{MHz}}{10^{6}\; \cancel{s^{-1}}} \right )=2.965\; m \)

As the police officer was writing up your speeding ticket, she mentioned that she was using a state-of-the-art radar gun operating at 35.5 GHz. What is the wavelength of the radiation emitted by the radar gun?

Answer: 8.45 mm

In Section 2.2 "The Quantization of Energy" and Section 2.3 "Atomic Spectra and Models of the Atom" , we describe how scientists developed our current understanding of the structure of atoms using the scientific method described in Chapter 1 "Introduction to Chemistry" . You will discover why scientists had to rethink their classical understanding of the nature of electromagnetic energy, which clearly distinguished between the particulate behavior of matter and the wavelike nature of energy.

Key Equations

relationship between wavelength, frequency, and speed of a wave

Equation 2.1.1 : \( v=\lambda \nu \)

relationship between wavelength, frequency, and speed of electromagnetic radiation

Equation 2.1.2 : \( c=\lambda \nu \)

A basic knowledge of the electronic structure of atoms requires an understanding of the properties of waves and electromagnetic radiation. A wave is a periodic oscillation by which energy is transmitted through space. All waves are periodic , repeating regularly in both space and time. Waves are characterized by several interrelated properties: wavelength (λ) , the distance between successive waves; frequency (ν) , the number of waves that pass a fixed point per unit time; speed ( v ) , the rate at which the wave propagates through space; and amplitude , the magnitude of the oscillation about the mean position. The speed of a wave is equal to the product of its wavelength and frequency. Electromagnetic radiation consists of two perpendicular waves, one electric and one magnetic, propagating at the speed of light ( c ) . Electromagnetic radiation is radiant energy that includes radio waves, microwaves, visible light, x-rays, and gamma rays, which differ only in their frequencies and wavelengths.

Key Takeaway

Understanding the electronic structure of atoms requires an understanding of the properties of waves and electromagnetic radiation.

Conceptual Problems

What are the characteristics of a wave? What is the relationship between electromagnetic radiation and wave energy?

At constant wavelength, what effect does increasing the frequency of a wave have on its speed? its amplitude?

List the following forms of electromagnetic radiation in order of increasing wavelength: x-rays, radio waves, infrared waves, microwaves, ultraviolet waves, visible waves, and gamma rays. List them in order of increasing frequency. Which has the highest energy?

A large industry is centered on developing skin-care products, such as suntan lotions and cosmetics, that cannot be penetrated by ultraviolet radiation. How does the wavelength of visible light compare with the wavelength of ultraviolet light? How does the energy of visible light compare with the energy of ultraviolet light? Why is this industry focused on blocking ultraviolet light rather than visible light?

Numerical Problems

The human eye is sensitive to what fraction of the electromagnetic spectrum, assuming a typical spectral range of 10 4 to 10 20 Hz? If we came from the planet Krypton and had x-ray vision (i.e., if our eyes were sensitive to x-rays in addition to visible light), how would this fraction be changed?

What is the frequency in megahertz corresponding to each wavelength?

1.77 × 10 3 km
9.88 Å
3.7 × 10 −10 m
5.8 × 10 −7 m
2.3 Å
8.6 × 10 7 m

Line spectra are also observed for molecular species. Given the following characteristic wavelengths for each species, identify the spectral region (ultraviolet, visible, etc.) in which the following line spectra will occur. Given 1.00 mol of each compound and the wavelength of absorbed or emitted light, how much energy does this correspond to?

NH 3 , 1.0 × 10 −2 m
CH 3 CH 2 OH, 9.0 μm
Mo atom, 7.1 Å

What is the speed of a wave in meters per second that has a wavelength of 1250 m and a frequency of 2.36 × 10 5 s −1 ?

A wave travels at 3.70 m/s with a frequency of 4.599 × 10 7 Hz and an amplitude of 1.0 m. What is its wavelength in nanometers?

An AM radio station broadcasts with a wavelength of 248.0 m. What is the broadcast frequency of the station in kilohertz? An AM station has a broadcast range of 92.6 MHz. What is the corresponding wavelength range in meters for this reception?

An FM radio station broadcasts with a wavelength of 3.21 m. What is the broadcast frequency of the station in megahertz? An FM radio typically has a broadcast range of 82–112 MHz. What is the corresponding wavelength range in meters for this reception?

A microwave oven operates at a frequency of approximately 2450 MHz. What is the corresponding wavelength? Water, with its polar molecules, absorbs electromagnetic radiation primarily in the infrared portion of the spectrum. Given this fact, why are microwave ovens used for cooking food?

Contributors

Modified by Joshua Halpern

Light Speed Video from Doc Schuster on YouTube

Wave Video from JaHuProductions on YouTube

Wavelength and Frequency from Oxford Academic on YouTube

The Nature of Sound

Introduction.

Sound is a longitudinal, mechanical wave.

Sound can travel through any medium, but it cannot travel through a vacuum. There is no sound in outer space.

Sound is a variation in pressure. A region of increased pressure on a sound wave is called a compression (or condensation). A region of decreased pressure on a sound wave is called a rarefaction (or dilation).

The sources of sound

vibrating solids
rapid expansion or compression (explosions and implosions)
Smooth (laminar) air flow around blunt obstacles may result in the formation of vortices (the plural of vortex) that snap off or shed with a characteristic frequency. This process is called vortex shedding and is another means by which sound waves are formed. This is how a whistle or flute produces sound. Also the aeolian harp effect of singing power lines and fluttering venetian blinds.

What are the different characteristics of a wave? What are the things that can be measured about waves? Amplitude, frequency (and period), wavelength, speed, and maybe phase. Deal with each one in that order.

amplitude, intensity, loudness, volume

Amplitude goes with intensity, loudness, or volume. That's the basic idea. The details go in a separate section .

[ISO 226:2003]

Unlike our ears and hydrophones, fish ears don't detect sound pressure, which is the compression of molecules. Instead, they perceive something called particle motion, the tiny back-and-forth movements of particles in response to sound waves.

speed of sound

The speed of sound depends upon the type of medium and its state. Sound generally travels faster in solids than in liquids than in gases.

The speed of sound in a medium is generally affected by two things: elasticity and inertia. This is the Newton-Laplace equation. Laplace added the γ (gamma) correction factor for ideal gases.

For solids…

For fluids (which incudes liquids and gases)…

For ideal gases…

Hi there. The speed of sound is faster in solids that have some stiffness like steel and slower in those that are softer like rubber.

Basically liquids. Actually, basically water.

The speed of sound in water is somewhat difficult to determine since it is affected by temperature, pressure, density, and salinity (or the amount of any other other dissolved substances). The speed of sound in water can be found using this emprically derived equation …

v = 1449.2 + 4.6 T − 0.055 T 2 + 0.00029 T 3 + (1.34 − 0.010 T )( s − 35) + 0.16 h

Generally, an increase in temperature and salinity will increase the speed of sound in water. Usually, ocean salinity is estimated at around 35 ppt, so the equation above is essentialy a function of temperature and depth.

Acoustic Thermometry of Ocean Climates (ATOC)

in water, sounds below 1 kHz travel much farther than higher frequencies
shipping noise is loudest in the 30 to 200 Hz range [lowest piano note to middle of cello]
blue and fin wales are the loudest sound in the 17 to 30 Hz range
"In pre-industrial times, the low frequency range of 15 to 300 Hz in which most of the baleen whales sing was the quietest part of the sound spectrum, nestled between the subsonic ramblings of earthquakes and the higher pitched rattle of wind, waves and rain." Bob Holmes. "Noises Off." New Scientist. 1 March 1997: 30–33.

ideal gases

Let's be honest. All we really care about is the speed of sound in air.

The speed of sound in air is approximately 345 m/s (about 1250 kph, 770 mph, 1100 ft/s).
The speed of sound in air is nearly the same for all frequencies and amplitudes.
It increases with temperature.

The speed of sound in air as a function of temperature can be found using these approximate equations…

the linear one
the one with the square root in it

Where should this go?

frequency, pitch, tone

The frequency of a sound wave is called it pitch . High frequency sounds are said to be "high pitched" or just "high"; low frequency sounds are said to be "low pitched" or just "low".

human hearing and speech

Humans are generally capable of hearing sounds between 20 Hz and 20 kHz (although I can't hear sounds above 13 kHz). Sounds with frequencies above the range of human hearing are called ultrasound . Sounds with frequencies below the range of human hearing are called infrasound .

Typical sounds produced by human speech have frequencies on the order of 100 to 1,000 Hz.
The peak sensitivity of human hearing is around 4,000 Hz.
Interaural Time Difference (ITD)
Interaural Phase Difference (IPD) Phase differences are one way we localize sounds. Only effective for wavelengths greater than 2 head diameters (ear-to-ear distances).
Interaural Level Difference (ILD) Sound waves diffract easily at wavelengths larger than the diameter of the human head (around 500 Hz wavelength equals 69 cm). At higher frequencies the head casts a "shadow". Sounds in one ear will be louder than the other.
1,400 different pitches
(whistle register?)
modal — the usual speaking register
vocal fry — the lowest of the three vocal registers

17.7: Ultrasound

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Learning Objectives

By the end of this section, you will be able to:

Define acoustic impedance and intensity reflection coefficient.
Describe medical and other uses of ultrasound technology.
Calculate acoustic impedance using density values and the speed of ultrasound.
Calculate the velocity of a moving object using Doppler-shifted ultrasound.

Any sound with a frequency above 20,000 Hz (or 20 kHz)—that is, above the highest audible frequency—is defined to be ultrasound. In practice, it is possible to create ultrasound frequencies up to more than a gigahertz. (Higher frequencies are difficult to create; furthermore, they propagate poorly because they are very strongly absorbed.) Ultrasound has a tremendous number of applications, which range from burglar alarms to use in cleaning delicate objects to the guidance systems of bats. We begin our discussion of ultrasound with some of its applications in medicine, in which it is used extensively both for diagnosis and for therapy.

An ultrasound image of a 21 week old fetus.

Characteristics of Ultrasound

Ultrasound in Medical Therapy

Ultrasound, like any wave, carries energy that can be absorbed by the medium carrying it, producing effects that vary with intensity. When focused to intensities of \(10^3\) to \(10^5 \, W/m^2\) ultrasound can be used to shatter gallstones or pulverize cancerous tissue in surgical procedures (Figure \(\PageIndex{2}\)). Intensities this great can damage individual cells, variously causing their protoplasm to stream inside them, altering their permeability, or rupturing their walls through cavitation . Cavitation is the creation of vapor cavities in a fluid—the longitudinal vibrations in ultrasound alternatively compress and expand the medium, and at sufficient amplitudes the expansion separates molecules. Most cavitation damage is done when the cavities collapse, producing even greater shock pressures.

A picture of a brain tumor being removed from the skull using a clinical probe.

Most of the energy carried by high-intensity ultrasound in tissue is converted to thermal energy. In fact, intensities of \(10^3\) to \(10^4 \, W/m^2\) are commonly used for deep-heat treatments called ultrasound diathermy. Frequencies of 0.8 to 1 MHz are typical. In both athletics and physical therapy, ultrasound diathermy is most often applied to injured or overworked muscles to relieve pain and improve flexibility. Skill is needed by the therapist to avoid “bone burns” and other tissue damage caused by overheating and cavitation, sometimes made worse by reflection and focusing of the ultrasound by joint and bone tissue.

In some instances, you may encounter a different decibel scale, called the sound pressure level, when ultrasound travels in water or in human and other biological tissues. We shall not use the scale here, but it is notable that numbers for sound pressure levels range 60 to 70 dB higher than you would quote for \(β\), the sound intensity level used in this text. Should you encounter a sound pressure level of 220 decibels, then, it is not an astronomically high intensity, but equivalent to about 155 dB—high enough to destroy tissue, but not as unreasonably high as it might seem at first.

Ultrasound in Medical Diagnostics

When used for imaging, ultrasonic waves are emitted from a transducer, a crystal exhibiting the piezoelectric effect (the expansion and contraction of a substance when a voltage is applied across it, causing a vibration of the crystal). These high-frequency vibrations are transmitted into any tissue in contact with the transducer. Similarly, if a pressure is applied to the crystal (in the form of a wave reflected off tissue layers), a voltage is produced which can be recorded. The crystal therefore acts as both a transmitter and a receiver of sound. Ultrasound is also partially absorbed by tissue on its path, both on its journey away from the transducer and on its return journey. From the time between when the original signal is sent and when the reflections from various boundaries between media are received, (as well as a measure of the intensity loss of the signal), the nature and position of each boundary between tissues and organs may be deduced.

Reflections at boundaries between two different media occur because of differences in a characteristic known as the acoustic impedance \(Z\) of each substance. Impedance is defined as

\[Z = \rho v,\]

where \(\rho\) is the density of the medium (in kg/m^3\) ) and \(v\) is the speed of sound through the medium (in m/s). The units for \(Z\) are therefore \(kg/(m^2 \cdot s)\).

Table \(\PageIndex{1}\) shows the density and speed of sound through various media (including various soft tissues) and the associated acoustic impedances. Note that the acoustic impedances for soft tissue do not vary much but that there is a big difference between the acoustic impedance of soft tissue and air and also between soft tissue and bone.

At the boundary between media of different acoustic impedances, some of the wave energy is reflected and some is transmitted. The greater the difference in acoustic impedance between the two media, the greater the reflection and the smaller the transmission.

The intensity reflection coefficien t \(a\) is defined as the ratio of the intensity of the reflected wave relative to the incident (transmitted) wave. This statement can be written mathematically as

\[a = \frac{\left(Z_{2} - Z_{1}\right)^2}{\left(Z_{1} + Z_{2}\right)^{2}},\]

where \(Z_{1}\) and \(Z_{2}\) are the acoustic impedances of the two media making up the boundary. A reflection coefficient of zero (corresponding to total transmission and no reflection) occurs when the acoustic impedances of the two media are the same. An impedance “match” (no reflection) provides an efficient coupling of sound energy from one medium to another. The image formed in an ultrasound is made by tracking reflections (as shown in Figure \(\PageIndex{3}\)) and mapping the intensity of the reflected sound waves in a two-dimensional plane.

Example \(\PageIndex{1}\): Calculate Acoustic Impedance and Intensity Reflection Coefficient: Ultrasound and Fat Tissue

(a) Using the values for density and the speed of ultrasound given in Table \(\PageIndex{1}\), show that the acoustic impedance of fat tissue is indeed \(1.34 \times 10^{6}kg / \left( m^{2} \cdot s \right)\).

(b) Calculate the intensity reflection coefficient of ultrasound when going from fat to muscle tissue.

Strategy for (a)

The acoustic impedance can be calculated using \(Z = \rho v\) and the values for \(\rho\) and \(v\) found in Table \(\PageIndex{1}\).

Solution for (a)

(1) Substitute known values from Table \(\PageIndex{1}\) into \(Z = \rho v\).

\[Z = \rho v = \left(925 kg/m^{3}\right)\left(1450 m/s\right)\]

(2) Calculate to find the acoustic impedance of fat tissue.

\[1.34 \times 10^{6} kg/\left(m^{2} \cdot s\right)\]

This value is the same as the value given for the acoustic impedance of fat tissue.

The intensity reflection coefficient for any boundary between two media is given by \(a = \frac{\left(Z_{2} - Z_{1}\right)^{2}}{\left(Z_{2} + Z_{1}\right)^{2}}\), and the acoustic impedance of muscle is given in Table \(\PageIndex{1}\).

Solution for (b)

Substitute known values into \(a = \frac{\left(Z_{2} - Z_{1}\right)^{2}}{\left(Z_{2} + Z_{1}\right)^{2}}\) to find the intensity reflection coefficient:

\[a = \frac{\left(Z_{2} - Z_{1}\right)^{2}}{\left(Z_{2} + Z_{1}\right)^{2}} = \frac{\left(1.34 \times 10^{6} kg/\left(m^{2} \cdot s\right) - 1.70 \times 10^{6} kg/\left(m^{2} \cdot s\right) \right)^{2}}{\left(1.70 \times 10^{6} kg / \left(m^{2}\cdot s\right) + 1.34 \times 10^{6} kg/ \left(m^{2} \cdot s \right) \right)^{2}} = 0.014\]

This result means that only 1.4% of the incident intensity is reflected, with the remaining being transmitted.

The applications of ultrasound in medical diagnostics have produced untold benefits with no known risks. Diagnostic intensities are too low (about \(10^{-2} W/m^{2}\)) to cause thermal damage. More significantly, ultrasound has been in use for several decades and detailed follow-up studies do not show evidence of ill effects, quite unlike the case for x-rays.

The first part of the diagram shows a rectangular shaped transducer with speaker and microphone sending spherical waves to produce echos from a fetus. The second part shows a graph of echo intensity versus time, with four sharp peaks.

The most common ultrasound applications produce an image like that shown in Figure \(\PageIndex{4}\). The speaker-microphone broadcasts a directional beam, sweeping the beam across the area of interest. This is accomplished by having multiple ultrasound sources in the probe’s head, which are phased to interfere constructively in a given, adjustable direction. Echoes are measured as a function of position as well as depth. A computer constructs an image that reveals the shape and density of internal structures.

The first part of the diagram shows an ultrasound device scanning a woman’s abdomen. The second part of the diagram is an ultrasound scan report of the abdomen.

How much detail can ultrasound reveal? The image in Figure \(\PageIndex{4}\) is typical of low-cost systems, but that in \(\PageIndex{5}\) shows the remarkable detail possible with more advanced systems, including 3D imaging. Ultrasound today is commonly used in prenatal care. Such imaging can be used to see if the fetus is developing at a normal rate, and help in the determination of serious problems early in the pregnancy. Ultrasound is also in wide use to image the chambers of the heart and the flow of blood within the beating heart, using the Doppler effect (echocardiology).

Whenever a wave is used as a probe, it is very difficult to detect details smaller than its wavelength \(\lambda\). Indeed, current technology cannot do quite this well. Abdominal scans may use a 7-MHz frequency, and the speed of sound in tissue is about 1540 m/s -- so the wavelength limit to detail would be \(\lambda = \frac{v_{w}}{f} = \frac{1540 m/s}{7 \times 10^{6} Hz} = 0.22mm\). In practice, 1-mm detail is attainable, which is sufficient for many purposes. Higher-frequency ultrasound would allow greater detail, but it does not penetrate as well as lower frequencies do. The accepted rule of thumb is that you can effectively scan to a depth of about \(500 \lambda\) into tissue. For 7 MHz, this penetration limit is \(500 \times 0.22 mm\), which is 0.11 m. Higher frequencies may be employed in smaller organs, such as the eye, but are not practical for looking deep into the body.

This is an image of a 3D ultrasound scan of the fetus showing an unborn baby sucking its thumb.

In addition to shape information, ultrasonic scans can produce density information superior to that found in X-rays, because the intensity of a reflected sound is related to changes in density. Sound is most strongly reflected at places where density changes are greatest.

Another major use of ultrasound in medical diagnostics is to detect motion and determine velocity through the Doppler shift of an echo, known as Doppler-shifted ultrasound . This technique is used to monitor fetal heartbeat, measure blood velocity, and detect occlusions in blood vessels, for example. (See Figure \(\PageIndex{6}\).)

Doppler-shifted ultrasonic image of a partially occluded artery.

A clever technique is used to measure the Doppler shift in an echo. The frequency of the echoed sound is superimposed on the broadcast frequency, producing beats. The beat frequency is \(F_{B} = \vert f_{1} - f_{2} \vert \), and so it is directly proportional to the Doppler shift ( \(f_{1} - f_{2}\) ) and hence, the reflector’s velocity. The advantage in this technique is that the Doppler shift is small (because the reflector’s velocity is small), so that great accuracy would be needed to measure the shift directly. But measuring the beat frequency is easy, and it is not affected if the broadcast frequency varies somewhat. Furthermore, the beat frequency is in the audible range and can be amplified for audio feedback to the medical observer.

USES FOR DOPPLER-SHIFTED RADAR

Doppler-shifted radar echoes are used to measure wind velocities in storms as well as aircraft and automobile speeds. The principle is the same as for Doppler-shifted ultrasound. There is evidence that bats and dolphins may also sense the velocity of an object (such as prey) reflecting their ultrasound signals by observing its Doppler shift.

Example \(\PageIndex{2}\): Calculate Velocity of Blood: Doppler-Shifted Ultrasound

Ultrasound that has a frequency of 2.50 MHz is sent toward blood in an artery that is moving toward the source at 20.0 cm/s, as illustrated in Figure \(\PageIndex{7}\). Use the speed of sound in human tissue as 1540 m/s. (Assume that the frequency of 2.50 MHz is accurate to seven significant figures.)

What frequency does the blood receive?
What frequency returns to the source?
What beat frequency is produced if the source and returning frequencies are mixed?

The picture represents an ultrasound device scanning the arteries and veins of a human hand.

The first two questions can be answered using \(f_{obs} = f_{s} \left(\frac{v_{w}}{v_{w} \pm v_{s}}\right)\) and \(f_{obs} = f_{s} \left(\frac{v_{w} \pm v_{obs}}{v_{w}}\right)\) for the Doppler shift. The last question asks for beat frequency, which is the difference between the original and returning frequencies.

The blood is a moving observer, and so the frequency it receives is given by \[f_{obs} = f_{s} \left(\frac{v_{w} \pm v_{obs}}{v_{w}}\right)\].
\(v_{b}\) is the blood velocity (\(v_{obs}\) here) and the plus sign is chosen because the motion is toward the source.
Enter the given values into the equation. \[f_{obs} = \left(2,500,000 Hz\right) \left( \frac{1540 m/s + 0.2 m/s}{1540 m/s}\right)\]
Calculate to find the frequency: 2,500,325 Hz.
The blood acts as a moving source.
The microphone acts as a stationary observer.
\(f_{obs}\) is the frequency received by the speaker-microphone.
The source velocity is \(v_{b}\).
The minus sign is used because the motion is toward the observer.
Enter the given values into the equation: \[f_{obs} = \left(2,500,325 Hz\right) \left( \frac{1540 m/s}{1540 m/s - 0.200 m/s}\right)\]
Calculate to find the frequency returning to the source: 2,500,649 Hz.

Solution for (c)

The beat frequency is simply the absolute value of the difference between \(f_{s}\) and \(f_{obs}\) as stated in: \[f_{B} = \vert f_{obs} - f_{s}\vert.\]
Substitute known values: \[\vert 2,500,649 Hz - 2,500,000 Hz\vert\]
Calculate to find the beat frequency: 649 Hz.

The Doppler shifts are quite small compared with the original frequency of 2.50 MHz. It is far easier to measure the beat frequency than it is to measure the echo frequency with an accuracy great enough to see shifts of a few hundred hertz out of a couple of megahertz. Furthermore, variations in the source frequency do not greatly affect the beat frequency, because both \(f_{s}\) and \(f_{obs}\) would increase or decrease. Those changes subtract out in \(f_{B} = \vert f_{obs} - f_{s} \vert\).

INDUSTRIAL AND OTHER APPLICATIONS OF ULTRASOUND

Industrial, retail, and research applications of ultrasound are common. A few are discussed here. Ultrasonic cleaners have many uses. Jewelry, machined parts, and other objects that have odd shapes and crevices are immersed in a cleaning fluid that is agitated with ultrasound typically about 40 kHz in frequency. The intensity is great enough to cause cavitation, which is responsible for most of the cleansing action. Because cavitation-produced shock pressures are large and well transmitted in a fluid, they reach into small crevices where even a low-surface-tension cleaning fluid might not penetrate.

Sonar is a familiar application of ultrasound. Sonar typically employs ultrasonic frequencies in the range from 30.0 to 100 kHz. Bats, dolphins, submarines, and even some birds use ultrasonic sonar. Echoes are analyzed to give distance and size information both for guidance and finding prey. In most sonar applications, the sound reflects quite well because the objects of interest have significantly different density than the medium in which they travel. When the Doppler shift is observed, velocity information can also be obtained. Submarine sonar can be used to obtain such information, and there is evidence that some bats also sense velocity from their echoes.

Similarly, there are a range of relatively inexpensive devices that measure distance by timing ultrasonic echoes. Many cameras, for example, use such information to focus automatically. Some doors open when their ultrasonic ranging devices detect a nearby object, and certain home security lights turn on when their ultrasonic rangers observe motion. Ultrasonic “measuring tapes” also exist to measure such things as room dimensions. Sinks in public restrooms are sometimes automated with ultrasound devices to turn faucets on and off when people wash their hands. These devices reduce the spread of germs and can conserve water.

Ultrasound is used for nondestructive testing in industry and by the military. Because ultrasound reflects well from any large change in density, it can reveal cracks and voids in solids, such as aircraft wings, that are too small to be seen with x-rays. For similar reasons, ultrasound is also good for measuring the thickness of coatings, particularly where there are several layers involved.

Basic research in solid state physics employs ultrasound. Its attenuation is related to a number of physical characteristics, making it a useful probe. Among these characteristics are structural changes such as those found in liquid crystals, the transition of a material to a superconducting phase, as well as density and other properties.

These examples of the uses of ultrasound are meant to whet the appetites of the curious, as well as to illustrate the underlying physics of ultrasound. There are many more applications, as you can easily discover for yourself.

Exercise \(\PageIndex{1}\)

Why is it possible to use ultrasound both to observe a fetus in the womb and also to destroy cancerous tumors in the body?

Ultrasound can be used medically at different intensities. Lower intensities do not cause damage and are used for medical imaging. Higher intensities can pulverize and destroy targeted substances in the body, such as tumors.

The acoustic impedance is defined as \(Z = \rho v\), where \(\rho\) is the density of a medium through which the sound travels and \(v\) is the speed of sound through that medium.
The intensity reflection coefficient \(a\), a measure of the ratio of the intensity of the wave reflected off a boundary between two media relative to the intensity of the incident wave, is given by \(a = \frac{\left(Z_{2} - Z_{1}\right)^{2}}{\left(Z_{1} + Z_{2}\right)^{2}}\).
The intensity reflection coefficient is a unitless quantity.

Q & A / Science

Why do radio waves travel at the speed of light and not sound?

by How It Works Team · 06/07/2013

Radio waves are a form of electromagnetic radiation – the same phenomenon as light, X-rays and various other types of radiation, but with much longer wavelengths. As such, they travel at the speed of light (ie 300,000 kilometres/186,000 miles per second) – a lot faster than the 340 metres (1,125 feet) per second that sound itself moves through the air. It’s easy to be fooled by the fact that when you hear the word ‘radio’, you usually think of voices or music, but radio waves aren’t sounds themselves – just the medium used to broadcast an electronic signal from the studio to your hi-fi, which the speaker then turns back into the vibrations in the air which we hear.

Answered by Giles Sparrow.

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Waves, Light Waves, Sound Waves and Ultrasound (The Physics of)

First Online: 07 April 2018

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Mechanical waves (sound waves, waves on water) are a mechanism for transferring energy through a medium (the air or water) without transferring matter. Another definition is a periodic disturbance in some property of the medium, the medium itself remaining relatively at rest. Waves have the following measurable properties:

Wavelength (symbol λ ) is the distance between two successive crests (in metres, m). A typical value is ~500 nm for light and ~20 cm for sound.

Frequency ( f ) is the number of λ that passes by in 1 s (in hertz, Hz). Typical values are 500 THz for light and 500 Hz for sound. Frequency is related to pitch (for sound) and colour (for visible light).

Period ( T ) is the time it takes for one λ to pass by (in seconds, s).

Speed ( v ) is how fast a wave is moving in the direction of propagation (in metres per second, m/s). The speed of light travelling through air is 3 × 10 8 m/s, while for sound, speed in air is about 330 m/s. In tissue, sound moves faster, at about 1560 m/s.

Amplitude ( A ) is the maximum displacement from the mean (or rest) position. For example, the vertical distance between a trough and a crest of a wave in water is two times the amplitude. Amplitude (or intensity) is related to loudness of sound and brightness of light and to the amount of energy being carried by the wave.

Phase refers to how far out of step the oscillation of one part of a wave is when compared with another part. A phase of 0° or 360° means that the two parts are in step, while a phase difference of 180° means that the two points are completely out of step. Differences in phase between the sounds entering each ear allow us to localise the source of a sound.

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Caon, M. (2018). Waves, Light Waves, Sound Waves and Ultrasound (The Physics of). In: Examination Questions and Answers in Basic Anatomy and Physiology. Springer, Cham. https://doi.org/10.1007/978-3-319-75599-1_16

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17.2 Speed of Sound

Learning objectives.

By the end of this section, you will be able to:

Explain the relationship between wavelength and frequency of sound
Determine the speed of sound in different media
Derive the equation for the speed of sound in air
Determine the speed of sound in air for a given temperature

Sound, like all waves, travels at a certain speed and has the properties of frequency and wavelength. You can observe direct evidence of the speed of sound while watching a fireworks display ( Figure 17.4 ). You see the flash of an explosion well before you hear its sound and possibly feel the pressure wave, implying both that sound travels at a finite speed and that it is much slower than light.

The difference between the speed of light and the speed of sound can also be experienced during an electrical storm. The flash of lighting is often seen before the clap of thunder. You may have heard that if you count the number of seconds between the flash and the sound, you can estimate the distance to the source. Every five seconds converts to about one mile. The velocity of any wave is related to its frequency and wavelength by

where v is the speed of the wave, f is its frequency, and λ λ is its wavelength. Recall from Waves that the wavelength is the length of the wave as measured between sequential identical points. For example, for a surface water wave or sinusoidal wave on a string, the wavelength can be measured between any two convenient sequential points with the same height and slope, such as between two sequential crests or two sequential troughs. Similarly, the wavelength of a sound wave is the distance between sequential identical parts of a wave—for example, between sequential compressions ( Figure 17.5 ). The frequency is the same as that of the source and is the number of waves that pass a point per unit time.

Speed of Sound in Various Media

Table 17.1 shows that the speed of sound varies greatly in different media. The speed of sound in a medium depends on how quickly vibrational energy can be transferred through the medium. For this reason, the derivation of the speed of sound in a medium depends on the medium and on the state of the medium. In general, the equation for the speed of a mechanical wave in a medium depends on the square root of the restoring force, or the elastic property , divided by the inertial property ,

Also, sound waves satisfy the wave equation derived in Waves ,

Recall from Waves that the speed of a wave on a string is equal to v = F T μ , v = F T μ , where the restoring force is the tension in the string F T F T and the linear density μ μ is the inertial property. In a fluid, the speed of sound depends on the bulk modulus and the density,

The speed of sound in a solid depends on the Young’s modulus of the medium and the density,

In an ideal gas (see The Kinetic Theory of Gases ), the equation for the speed of sound is

where γ γ is the adiabatic index, R = 8.31 J/mol · K R = 8.31 J/mol · K is the gas constant, T K T K is the absolute temperature in kelvins, and M is the molar mass. In general, the more rigid (or less compressible) the medium, the faster the speed of sound. This observation is analogous to the fact that the frequency of simple harmonic motion is directly proportional to the stiffness of the oscillating object as measured by k , the spring constant. The greater the density of a medium, the slower the speed of sound. This observation is analogous to the fact that the frequency of a simple harmonic motion is inversely proportional to m , the mass of the oscillating object. The speed of sound in air is low, because air is easily compressible. Because liquids and solids are relatively rigid and very difficult to compress, the speed of sound in such media is generally greater than in gases.

Because the speed of sound depends on the density of the material, and the density depends on the temperature, there is a relationship between the temperature in a given medium and the speed of sound in the medium. For air at sea level, the speed of sound is given by

where the temperature in the first equation (denoted as T C T C ) is in degrees Celsius and the temperature in the second equation (denoted as T K T K ) is in kelvins. The speed of sound in gases is related to the average speed of particles in the gas, v rms = 3 k B T m , v rms = 3 k B T m , where k B k B is the Boltzmann constant ( 1.38 × 10 −23 J/K ) ( 1.38 × 10 −23 J/K ) and m is the mass of each (identical) particle in the gas. Note that v refers to the speed of the coherent propagation of a disturbance (the wave), whereas v rms v rms describes the speeds of particles in random directions. Thus, it is reasonable that the speed of sound in air and other gases should depend on the square root of temperature. While not negligible, this is not a strong dependence. At 0 °C 0 °C , the speed of sound is 331 m/s, whereas at 20.0 °C 20.0 °C , it is 343 m/s, less than a 4 % 4 % increase. Figure 17.6 shows how a bat uses the speed of sound to sense distances.

Derivation of the Speed of Sound in Air

As stated earlier, the speed of sound in a medium depends on the medium and the state of the medium. The derivation of the equation for the speed of sound in air starts with the mass flow rate and continuity equation discussed in Fluid Mechanics .

Consider fluid flow through a pipe with cross-sectional area A ( Figure 17.7 ). The mass in a small volume of length x of the pipe is equal to the density times the volume, or m = ρ V = ρ A x . m = ρ V = ρ A x . The mass flow rate is

The continuity equation from Fluid Mechanics states that the mass flow rate into a volume has to equal the mass flow rate out of the volume, ρ in A in v in = ρ out A out v out . ρ in A in v in = ρ out A out v out .

Now consider a sound wave moving through a parcel of air. A parcel of air is a small volume of air with imaginary boundaries ( Figure 17.8 ). The density, temperature, and velocity on one side of the volume of the fluid are given as ρ , T , v , ρ , T , v , and on the other side are ρ + d ρ , T + d T , v + d v . ρ + d ρ , T + d T , v + d v .

The continuity equation states that the mass flow rate entering the volume is equal to the mass flow rate leaving the volume, so

This equation can be simplified, noting that the area cancels and considering that the multiplication of two infinitesimals is approximately equal to zero: d ρ ( d v ) ≈ 0 , d ρ ( d v ) ≈ 0 ,

The net force on the volume of fluid ( Figure 17.9 ) equals the sum of the forces on the left face and the right face:

The acceleration is the force divided by the mass and the mass is equal to the density times the volume, m = ρ V = ρ d x d y d z . m = ρ V = ρ d x d y d z . We have

From the continuity equation ρ d v = − v d ρ ρ d v = − v d ρ , we obtain

Consider a sound wave moving through air. During the process of compression and expansion of the gas, no heat is added or removed from the system. A process where heat is not added or removed from the system is known as an adiabatic system. Adiabatic processes are covered in detail in The First Law of Thermodynamics , but for now it is sufficient to say that for an adiabatic process, p V γ = constant, p V γ = constant, where p is the pressure, V is the volume, and gamma ( γ ) ( γ ) is a constant that depends on the gas. For air, γ = 1.40 γ = 1.40 . The density equals the number of moles times the molar mass divided by the volume, so the volume is equal to V = n M ρ . V = n M ρ . The number of moles and the molar mass are constant and can be absorbed into the constant p ( 1 ρ ) γ = constant . p ( 1 ρ ) γ = constant . Taking the natural logarithm of both sides yields ln p − γ ln ρ = constant . ln p − γ ln ρ = constant . Differentiating with respect to the density, the equation becomes

If the air can be considered an ideal gas, we can use the ideal gas law:

Here M is the molar mass of air:

Since the speed of sound is equal to v = d p d ρ v = d p d ρ , the speed is equal to

Note that the velocity is faster at higher temperatures and slower for heavier gases. For air, γ = 1.4 , γ = 1.4 , M = 0.02897 kg mol , M = 0.02897 kg mol , and R = 8.31 J mol · K . R = 8.31 J mol · K . If the temperature is T C = 20 ° C ( T = 293 K ) , T C = 20 ° C ( T = 293 K ) , the speed of sound is v = 343 m/s . v = 343 m/s .

The equation for the speed of sound in air v = γ R T M v = γ R T M can be simplified to give the equation for the speed of sound in air as a function of absolute temperature:

One of the more important properties of sound is that its speed is nearly independent of the frequency. This independence is certainly true in open air for sounds in the audible range. If this independence were not true, you would certainly notice it for music played by a marching band in a football stadium, for example. Suppose that high-frequency sounds traveled faster—then the farther you were from the band, the more the sound from the low-pitch instruments would lag that from the high-pitch ones. But the music from all instruments arrives in cadence independent of distance, so all frequencies must travel at nearly the same speed. Recall that

In a given medium under fixed conditions, v is constant, so there is a relationship between f and λ ; λ ; the higher the frequency, the smaller the wavelength ( Figure 17.10 ).

Example 17.1

Calculating wavelengths.

Identify knowns. The value for v is given by v = ( 331 m/s ) T 273 K . v = ( 331 m/s ) T 273 K .
Convert the temperature into kelvins and then enter the temperature into the equation v = ( 331 m/s ) 303 K 273 K = 348.7 m/s . v = ( 331 m/s ) 303 K 273 K = 348.7 m/s .
Solve the relationship between speed and wavelength for λ : λ = v f . λ = v f .
Enter the speed and the minimum frequency to give the maximum wavelength: λ max = 348.7 m/s 20 Hz = 17 m . λ max = 348.7 m/s 20 Hz = 17 m .
Enter the speed and the maximum frequency to give the minimum wavelength: λ min = 348.7 m/s 20,000 Hz = 0.017 m = 1.7 cm . λ min = 348.7 m/s 20,000 Hz = 0.017 m = 1.7 cm .

Significance

The speed of sound can change when sound travels from one medium to another, but the frequency usually remains the same. This is similar to the frequency of a wave on a string being equal to the frequency of the force oscillating the string. If v changes and f remains the same, then the wavelength λ λ must change. That is, because v = f λ v = f λ , the higher the speed of a sound, the greater its wavelength for a given frequency.

Check Your Understanding 17.1

Imagine you observe two firework shells explode. You hear the explosion of one as soon as you see it. However, you see the other shell for several milliseconds before you hear the explosion. Explain why this is so.

Although sound waves in a fluid are longitudinal, sound waves in a solid travel both as longitudinal waves and transverse waves. Seismic waves , which are essentially sound waves in Earth’s crust produced by earthquakes, are an interesting example of how the speed of sound depends on the rigidity of the medium. Earthquakes produce both longitudinal and transverse waves, and these travel at different speeds. The bulk modulus of granite is greater than its shear modulus. For that reason, the speed of longitudinal or pressure waves (P-waves) in earthquakes in granite is significantly higher than the speed of transverse or shear waves (S-waves). Both types of earthquake waves travel slower in less rigid material, such as sediments. P-waves have speeds of 4 to 7 km/s, and S-waves range in speed from 2 to 5 km/s, both being faster in more rigid material. The P-wave gets progressively farther ahead of the S-wave as they travel through Earth’s crust. The time between the P- and S-waves is routinely used to determine the distance to their source, the epicenter of the earthquake. Because S-waves do not pass through the liquid core, two shadow regions are produced ( Figure 17.11 ).

Seismologists and geophysicists use properties and velocities of earthquake waves to study the Earth's interior, which due to it's depth and pressure is not observable through many other means. In fact, the discoveries of the structure of the Earth, illustrated in the figure above, resulted from earthquake observations. In 1914, Beno Gutenberg used differences in wave speeds to determine that there must be a liquid core within the mantle. In 1936, Inge Lehmann began investigating P-waves from a New Zealand earthquake that had unexpectedly reached Europe, which should have been in the shadow region. Up until that point, seismologists had explained such shadow waves as being caused by some type of diffraction (as Gutenberg himself assumed) or a result of faulty seismometers. However, Lehmann had installed the European instruments herself, and so trusted their accuracy. She calculated that the amplitude of the waves must be caused by the existence of a solid inner core within the liquid core. This model has been accepted and reinforced by decades of subsequent calculations, including those from nuclear test explosions, which can be measured very precisely.

As sound waves move away from a speaker, or away from the epicenter of an earthquake, their power per unit area decreases. This is why the sound is very loud near a speaker and becomes less loud as you move away from the speaker. This also explains why there can be an extreme amount of damage at the epicenter of an earthquake but only tremors are felt in areas far from the epicenter. The power per unit area is known as the intensity, and in the next section, we will discuss how the intensity depends on the distance from the source.

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A rock perched on an outcrop in Antarctica, with am ice pick for size comparison.

A clock in the rocks: what cosmic rays tell us about Earth’s changing surface and climate

Senior Lecturer in Physical Geography, Te Herenga Waka — Victoria University of Wellington

Assistant Director Polar Rock Repository, Byrd Polar and Climate Research Center, The Ohio State University

Associate Professor in Geochemistry, Te Herenga Waka — Victoria University of Wellington

PhD candidate, University of Canterbury

Disclosure statement

Shaun Eaves receives funding from the New Zealand Antarctic Science Platform.

Jamey Stutz receives funding from the New Zealand Antarctic Science Platform and the United States National Science Foundation .

Kevin Norton receives funding from Te Apārangi.

Pedro Doll receives funding from the Resilience to Nature national science challenge.

The Ohio State University provides funding as a founding partner of The Conversation US.

Te Herenga Waka — Victoria University of Wellington and University of Canterbury provide funding as members of The Conversation NZ.

University of Canterbury and Te Herenga Waka—Victoria University of Wellington provide funding as members of The Conversation AU.

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How often do mountains collapse, volcanoes erupt or ice sheets melt?

For Earth scientists, these are important questions as we try to improve projections to prepare communities for hazardous events in the future.

We rely on instrumental measurements, but such records are often short. To extend these, we use geological archives. And at the heart of this research is geochronology – a toolkit of geological dating methods that allow us to assign absolute ages to rocks.

Scientists standing on a bluff to examine rocks in Antarctica

In recent years, we have been using a state-of-the-art technique known as cosmogenic surface exposure dating which allows us to quantify the time a rock has spent on the surface, exposed to signals from outer space.

Using cosmic rays as a clock

Earth is constantly bombarded by high-energy charged particles, known as cosmic rays, coming from the depths of our galaxy. Most are intercepted by Earth’s magnetic field and atmosphere. But some are sufficiently energetic to reach Earth’s surface.

On impact, they break apart atoms of common elements in Earth’s crust, such as silicon and oxygen, to create new rare elements known as cosmogenic nuclides.

The presence of cosmogenic nuclides in rocks and sediments at the Earth’s surface is a clear indicator of atmospheric exposure. Their abundance tells us how long the rock has been exposed.

Schematic diagram of cosmogenic nuclide production by cosmic rays

Cosmic rays were first discovered in the early 1900s , but it took almost a century until sufficiently sensitive particle accelerators became available to accurately count the small number of rare atoms produced when they hit Earth.

Today, cosmogenic surface exposure dating represents a primary technique for quantifying the rates and dates of several processes on Earth’s surface.

Timing mountain collapse

In southeast Fiordland, the Green Lake landslide is one of the largest landslides on Earth. Its large size is especially unusual given the relatively small stature of the mountains from which it came.

Aerial photograph of an ancient landslide deposit now covered in trees

Previous research suggested the landslide was induced by the retreat of a large glacier that formerly supported the mountainside.

Given ongoing glacial retreat today, we sought to test this hypothesis by collecting boulders on the surface of the Green Lake landslide. These rocks had previously been shielded from cosmic rays in the mountain interior before becoming exposed by the landslide.

Our measurements yielded an exposure age of about 15,500 years , which postdates the end of the last ice age in the Southern Alps by 3,000 to 4,000 years. From this result, we conclude that deglaciation is unlikely to have been the primary cause of this spectacular mountain collapse. Instead, our findings point to an extremely large earthquake as the more likely trigger.

How often do volcanoes emit lava?

Effusive (lava-producing) volcanic eruptions have built the large cone of Mt Ruapehu, the highest mountain in the North Island.

Despite some explosive episodes during the 20th century, there is no observational record of eruptions producing lava flows. Future effusive events could fundamentally reshape the volcanic cone, with potential implications for local infrastructure.

But how often do such eruptions happen?

Scientist sitting on an outcrop, recording notes about a rock sample

Supported by the Resilience to Nature national science challenge , we tested whether cosmogenic dating could help us determine recurrence intervals of lava-producing eruptions on Mt Ruapehu over the past 20,000 years.

We found the mountain ejected lava in clusters of eruptive activity which could last for millennia. The cosmogenic data also provided more precise dates for recent prehistoric eruptions, compared to those produced by other common volcanic dating techniques such as palaeomagnetic and radiometric methods.

Tracking the melting of ice

Before cosmogenic nuclide measurements, glacial geologists trying to determine the age of sediments relied on serendipitous discoveries of fossil plant material for radiocarbon dating. In alpine and polar regions, where most glaciers are, such matter is rarely available.

Cosmogenic nuclides solve this problem as glaciers quarry rocks from their base and transport them to the surface where they rest on hill slopes and moraines and begin accumulating their cosmic signal.

With support from the New Zealand Antarctic Science Platform , we have applied this technique to reconstruct the recent evolution of Byrd Glacier – a large outlet of the East Antarctic Ice Sheet.

Glacial cobbles, transported from the Antarctic interior and deposited on hillsides on either side of the flowing glacier, track how high the glacier was in the past.

Our study shows that the glacier thinned by at least 200 metres about 7,000 years ago during an interval of relative global climate stability. These results provide rare three-dimensional information that can be used to evaluate computer models used to simulate past, present and future ice sheet change.

Lonewolf Nunataks, Byrd Glacier, East Antarctica

Rising sea level is one of the biggest challenges facing civilisation this century. However, the uncertain response of ice sheets to climate change currently hampers projections.

Cosmogenic nuclide specialists are now ambitiously attempting to recover rock samples from beneath sensitive portions of the present ice sheets . Testing them for cosmic signals will yield important insights about the potential of future melting of ice sheets.

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15.1 The Electromagnetic Spectrum
14.1 Speed of Sound, Frequency, and Wavelength; 14.2 Sound Intensity ... The high-frequency radiation to the right of ultraviolet (UV) includes X-rays and gamma (γ) rays. Teacher Support. ... EM waves mentioned above are basically the same form of radiation. They can all travel across empty space, and they all travel at the speed of light in a ...
24.3 The Electromagnetic Spectrum
17.1 Sound; 17.2 Speed of Sound, Frequency, and Wavelength; 17.3 Sound Intensity and Sound Level; ... FM, and cell phones, and account for some of the differences in how they are broadcast and how well they travel. ... X-rays are also used as a precise tool for trace-metal analysis in X-ray induced fluorescence, in which the energy of the X-ray ...
Electromagnetic Radiation
The speed of light is always a constant (3 x 10^8 m/s) ... Mechanical waves require a medium (matter) to travel through. Examples are sound waves, water waves, ripples in strings or springs. Water Waves. ... The areas where x-rays do not strike will form the image of the bone. While the principles remain the same, x-ray machines today use ...
Speed of Sound in Physics
Speed of Sound in Physics. This entry was posted on June 17, 2023 by Anne Helmenstine (updated on June 22, 2023) The speed of sound in dry air at room temperature is 343 m/s or 1125 ft/s. In physics, the speed of sound is the distance traveled per unit of time by a sound wave through a medium. It is highest for stiff solids and lowest for gases.
17.2: Speed of Sound, Frequency, and Wavelength
The relationship of the speed of sound, its frequency, and wavelength is the same as for all waves: vw = fλ, (17.2.1) (17.2.1) v w = f λ, where vw v w is the speed of sound, f f is its frequency, and λ λ is its wavelength. The wavelength of a sound is the distance between adjacent identical parts of a wave—for example, between adjacent ...
16.2: Traveling Waves
Examples include gamma rays, X-rays, ultraviolet waves, visible light, infrared waves, microwaves, and radio waves. Electromagnetic waves can travel through a vacuum at the speed of light, v = c = 2.99792458 x 10 8 m/s. For example, light from distant stars travels through the vacuum of space and reaches Earth.
Speed of Sound (video)
In non-humid air at 20 degrees Celsius, the speed of sound is about 343 meters per second or 767 miles per hour. We can also watch the speed of sound of a repeating simple harmonic wave. The speed of the wave can again be determined by the speed of the compressed regions as they travel through the medium.
Light: Electromagnetic waves, the electromagnetic spectrum and photons
Electromagnetic radiation is one of the many ways that energy travels through space. The heat from a burning fire, the light from the sun, the X-rays used by your doctor, as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation. While these forms of energy might seem quite different from one another ...
Physics Tutorial: The Speed of Sound
The speed of a sound wave refers to how fast a sound wave is passed from particle to particle through a medium. The speed of a sound wave in air depends upon the properties of the air - primarily the temperature. Sound travels faster in solids than it does in liquids; sound travels slowest in gases such as air. The speed of sound can be calculated as the distance-per-time ratio or as the ...
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A combination of radio waves and strong magnetic fields is used by magnetic resonance imaging (MRI) to produce diagnostic pictures of parts of the human body and brain without apparent harmful effects. This imaging technique has thus found increasingly wider application in medicine ( see also radiation ). Extremely low-frequency (ELF) waves are ...
Speed of sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At 20 °C (68 °F), the speed of sound in air is about 343 m/s (1,125 ft/s; 1,235 km/h; 767 mph; 667 kn), or one km in 2.91 s or one mile in 4.69 s.It depends strongly on temperature as well as the medium through which a sound wave is propagating.
Chapter 2.1: Waves and Electromagnetic Radiation
In a vacuum, all forms of electromagnetic radiation—whether microwaves, visible light, or gamma rays—travel at the speed of light (c) The speed with which all forms of electromagnetic radiation travel in a vacuum., a fundamental physical constant with a value of 2.99792458 × 10 8 m/s (which is about 3.00 ×10 8 m/s or 1.86 × 10 5 mi/s ...
16.1 Traveling Waves
Examples include gamma rays, X-rays, ultraviolet waves, visible light, infrared waves, microwaves, and radio waves. Electromagnetic waves can travel through a vacuum at the speed of light, v = c = 2.99792458 × 10 8 m/s. v = c = 2.99792458 × 10 8 m/s. For example, light from distant stars travels through the vacuum of space and reaches Earth.
The Nature of Sound
speed of sound The speed of sound depends upon the type of medium and its state. Sound generally travels faster in solids than in liquids than in gases. The speed of sound in a medium is generally affected by two things: elasticity and inertia. This is the Newton-Laplace equation. Laplace added the γ (gamma) correction factor for ideal gases.
17.7: Ultrasound
The debris is then aspirated. The speed of the tip may exceed the speed of sound in tissue, thus creating shock waves and cavitation, rather than a smooth simple harmonic oscillator-type wave. ... ultrasonic scans can produce density information superior to that found in X-rays, because the intensity of a reflected sound is related to changes ...
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Why do radio waves travel at the speed of light and not sound?
by How It Works Team · 06/07/2013. Radio waves are a form of electromagnetic radiation - the same phenomenon as light, X-rays and various other types of radiation, but with much longer wavelengths. As such, they travel at the speed of light (ie 300,000 kilometres/186,000 miles per second) - a lot faster than the 340 metres (1,125 feet) per ...
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Ultrasound Trumps X-Rays at Identifying Foreign Bodies. Dr. Buttsis the director of the division of emergency ultrasound and a clinical assistant professor of emergency medicine at Louisiana State University at New Orleans.Dr. Martinezis a third-year emergency medicine resident at LSU. Emergency Medicine News: March 2013 - Volume 35 - Issue 3 ...
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Sound is a mechanical wave, while light does not require a medium to travel in. B. Light is a transverse wave phenomenon, while sound is a longitudinal wave phenomenon. C. The speed of light is much greater than the speed of sound. D. Ultrasound and ultraviolet light have frequencies less than infrasound and infrared light.
17.2 Speed of Sound
Speed of Sound in Various Media. Table 17.1 shows that the speed of sound varies greatly in different media. The speed of sound in a medium depends on how quickly vibrational energy can be transferred through the medium. For this reason, the derivation of the speed of sound in a medium depends on the medium and on the state of the medium.
Radiography Worksheet Questions
X-rays travel at the speed of sound B. X-rays travel in a straight line with a wavelike motion C. X-rays have no electrical charge D. X-rays cause ionization, Which statement is correct? A. X-rays are a form of electromagnetic radiation; visible light is not B. X-rays have more energy than does visible light C. X-rays have a longer wavelength ...
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1. Appearance: invisible, undetectable by any of the senses 2. Mass: X-Rays have no mass or weight 3. Charge: X-rays have no charge 4. Speed: X-rays travel at the speed of light 5. Wavelength: Travel in waves and have short wavelengths with a high frequency 6. Path of Travel: Straight lines; deflected or scattered 7. Focusing Capability: Cannot be focused to a point & always diverge from a ...
A clock in the rocks: what cosmic rays tell us about Earth's changing
When landslides or glaciers bring rocks to the surface, cosmic rays bombard them, smashing common atoms into rarer forms and acting as a chronometer of the changing Earth.

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17.2 Speed of Sound

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