travelling wave features

Travelling Wave

When something about the physical world changes, the information about that disturbance gradually moves outwards, away from the source, in every direction. As the information travels, it travels in the form of a wave. Sound to our ears, light to our eyes, and electromagnetic radiation to our mobile phones are all transported in the form of waves. A good visual example of the propagation of waves is the waves created on the surface of the water when a stone is dropped into a lake. In this article, we will be learning more about travelling waves.

Describing a Wave

A wave can be described as a disturbance in a medium that travels transferring momentum and energy without any net motion of the medium. A wave in which the positions of maximum and minimum amplitude travel through the medium is known as a travelling wave. To better understand a wave, let us think of the disturbance caused when we jump on a trampoline. When we jump on a trampoline, the downward push that we create at a point on the trampoline slightly moves the material next to it downward too.

When the created disturbance travels outward, the point at which our feet first hit the trampoline recovers moving outward because of the tension force in the trampoline and that moves the surrounding nearby materials outward too. This up and down motion gradually ripples out as it covers more area of the trampoline. And, this disturbance takes the shape of a wave.

Following are a few important points to remember about the wave:

• The high points in the wave are known as crests and the low points in the wave are known as troughs.
• The maximum distance of the disturbance of the wave from the mid-point to either the top of the crest or to the bottom of a trough is known as amplitude.
• The distance between two adjacent crests or two adjacent troughs is known as a wavelength and is denoted by 𝛌.
• The time interval of one complete vibration is known as a time period.
• The number of vibrations the wave undergoes in one second is known as a frequency.
• The relationship between the time period and frequency is given as follows:
• The speed of a wave is given by the equation

Different Types of Waves

Different types of waves exhibit distinct characteristics. These characteristics help us distinguish between wave types. The orientation of particle motion relative to the direction of wave propagation is one way the traveling waves are distinguished. Following are the different types of waves categorized based on the particle motion:

• Pulse Waves – A pulse wave is a wave comprising only one disturbance or only one crest that travels through the transmission medium.
• Continuous Waves – A continuous-wave is a waveform of constant amplitude and frequency.
• Transverse Waves – In a transverse wave, the motion of the particle is perpendicular to the direction of propagation of the wave.
• Longitudinal Waves – Longitudinal waves are the waves in which the motion of the particle is in the same direction as the propagation of the wave.

Although they are different, there is one property common between them and that is the transportation of energy. An object in simple harmonic motion has an energy of

Constructive and Destructive Interference

A phenomenon in which two waves superimpose to form a resultant wave of lower, greater, or the same amplitude is known as interference. Constructive and destructive interference occurs due to the interaction of waves that are correlated with each other either because of the same frequency or because they come from the same source. The interference effects can be observed in all types of waves such as gravity waves and light waves.

According to the principle of superposition of the waves , when two or more propagating waves of the same type are incidents on the same point, the resultant amplitude is equal to the vector sum of the amplitudes of the individual waves. When a crest of a wave meets a crest of another wave of the same frequency at the same point, then the resultant amplitude is the sum of the individual amplitudes. This type of interference is known as constructive interference. If a crest of a wave meets a trough of another wave, then the resulting amplitude is equal to the difference in the individual amplitudes and this is known as destructive interference.

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Watch the video and understand longitudinal and transverse waves in detail.

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16.1 Traveling Waves

Learning objectives.

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

• Describe the basic characteristics of wave motion
• Define the terms wavelength, amplitude, period, frequency, and wave speed
• Explain the difference between longitudinal and transverse waves, and give examples of each type
• List the different types of waves

We saw in Oscillations that oscillatory motion is an important type of behavior that can be used to model a wide range of physical phenomena. Oscillatory motion is also important because oscillations can generate waves, which are of fundamental importance in physics. Many of the terms and equations we studied in the chapter on oscillations apply equally well to wave motion ( (Figure) ).

Figure 16.2 From the world of renewable energy sources comes the electric power-generating buoy. Although there are many versions, this one converts the up-and-down motion, as well as side-to-side motion, of the buoy into rotational motion in order to turn an electric generator, which stores the energy in batteries.

Types of Waves

A wave is a disturbance that propagates, or moves from the place it was created. There are three basic types of waves: mechanical waves, electromagnetic waves, and matter waves.

Basic mechanical waves are governed by Newton’s laws and require a medium. A medium is the substance a mechanical waves propagates through, and the medium produces an elastic restoring force when it is deformed. Mechanical waves transfer energy and momentum, without transferring mass. Some examples of mechanical waves are water waves, sound waves, and seismic waves. The medium for water waves is water; for sound waves, the medium is usually air. (Sound waves can travel in other media as well; we will look at that in more detail in Sound .) For surface water waves, the disturbance occurs on the surface of the water, perhaps created by a rock thrown into a pond or by a swimmer splashing the surface repeatedly. For sound waves, the disturbance is a change in air pressure, perhaps created by the oscillating cone inside a speaker or a vibrating tuning fork. In both cases, the disturbance is the oscillation of the molecules of the fluid. In mechanical waves, energy and momentum transfer with the motion of the wave, whereas the mass oscillates around an equilibrium point. (We discuss this in Energy and Power of a Wave .) Earthquakes generate seismic waves from several types of disturbances, including the disturbance of Earth’s surface and pressure disturbances under the surface. Seismic waves travel through the solids and liquids that form Earth. In this chapter, we focus on mechanical waves.

Electromagnetic waves are associated with oscillations in electric and magnetic fields and do not require a medium. 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, [latex] v=c=2.99792458\,×\,{10}^{8}\,\text{m/s}. [/latex] For example, light from distant stars travels through the vacuum of space and reaches Earth. Electromagnetic waves have some characteristics that are similar to mechanical waves; they are covered in more detail in Electromagnetic Waves in volume 2 of this text.

Matter waves are a central part of the branch of physics known as quantum mechanics. These waves are associated with protons, electrons, neutrons, and other fundamental particles found in nature. The theory that all types of matter have wave-like properties was first proposed by Louis de Broglie in 1924. Matter waves are discussed in Photons and Matter Waves in the third volume of this text.

Mechanical Waves

Mechanical waves exhibit characteristics common to all waves, such as amplitude, wavelength, period, frequency, and energy. All wave characteristics can be described by a small set of underlying principles.

The simplest mechanical waves repeat themselves for several cycles and are associated with simple harmonic motion. These simple harmonic waves can be modeled using some combination of sine and cosine functions. For example, consider the simplified surface water wave that moves across the surface of water as illustrated in (Figure) . Unlike complex ocean waves, in surface water waves, the medium, in this case water, moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. In (Figure) , the waves causes a seagull to move up and down in simple harmonic motion as the wave crests and troughs (peaks and valleys) pass under the bird. The crest is the highest point of the wave, and the trough is the lowest part of the wave. The time for one complete oscillation of the up-and-down motion is the wave’s period T . The wave’s frequency is the number of waves that pass through a point per unit time and is equal to [latex] f=1\text{/}T. [/latex] The period can be expressed using any convenient unit of time but is usually measured in seconds; frequency is usually measured in hertz (Hz), where [latex] 1\,{\text{Hz}=1\,\text{s}}^{-1}. [/latex]

The length of the wave is called the wavelength and is represented by the Greek letter lambda [latex] (\lambda ) [/latex], which is measured in any convenient unit of length, such as a centimeter or meter. The wavelength can be measured between any two similar points along the medium that have the same height and the same slope. In (Figure) , the wavelength is shown measured between two crests. As stated above, the period of the wave is equal to the time for one oscillation, but it is also equal to the time for one wavelength to pass through a point along the wave’s path.

The amplitude of the wave ( A ) is a measure of the maximum displacement of the medium from its equilibrium position. In the figure, the equilibrium position is indicated by the dotted line, which is the height of the water if there were no waves moving through it. In this case, the wave is symmetrical, the crest of the wave is a distance [latex] \text{+}A [/latex] above the equilibrium position, and the trough is a distance [latex] \text{−}A [/latex] below the equilibrium position. The units for the amplitude can be centimeters or meters, or any convenient unit of distance.

Figure 16.3 An idealized surface water wave passes under a seagull that bobs up and down in simple harmonic motion. The wave has a wavelength [latex] \lambda [/latex], which is the distance between adjacent identical parts of the wave. The amplitude A of the wave is the maximum displacement of the wave from the equilibrium position, which is indicated by the dotted line. In this example, the medium moves up and down, whereas the disturbance of the surface propagates parallel to the surface at a speed v.

The water wave in the figure moves through the medium with a propagation velocity [latex] \overset{\to }{v}. [/latex] The magnitude of the wave velocity is the distance the wave travels in a given time, which is one wavelength in the time of one period, and the wave speed is the magnitude of wave velocity. In equation form, this is

This fundamental relationship holds for all types of waves. For water waves, v is the speed of a surface wave; for sound, v is the speed of sound; and for visible light, v is the speed of light.

Transverse and Longitudinal Waves

We have seen that a simple mechanical wave consists of a periodic disturbance that propagates from one place to another through a medium. In (Figure) (a), the wave propagates in the horizontal direction, whereas the medium is disturbed in the vertical direction. Such a wave is called a transverse wave . In a transverse wave, the wave may propagate in any direction, but the disturbance of the medium is perpendicular to the direction of propagation. In contrast, in a longitudinal wave or compressional wave, the disturbance is parallel to the direction of propagation. (Figure) (b) shows an example of a longitudinal wave. The size of the disturbance is its amplitude A and is completely independent of the speed of propagation v .

Figure 16.4 (a) In a transverse wave, the medium oscillates perpendicular to the wave velocity. Here, the spring moves vertically up and down, while the wave propagates horizontally to the right. (b) In a longitudinal wave, the medium oscillates parallel to the propagation of the wave. In this case, the spring oscillates back and forth, while the wave propagates to the right.

A simple graphical representation of a section of the spring shown in (Figure) (b) is shown in (Figure) . (Figure) (a) shows the equilibrium position of the spring before any waves move down it. A point on the spring is marked with a blue dot. (Figure) (b) through (g) show snapshots of the spring taken one-quarter of a period apart, sometime after the end of` the spring is oscillated back and forth in the x -direction at a constant frequency. The disturbance of the wave is seen as the compressions and the expansions of the spring. Note that the blue dot oscillates around its equilibrium position a distance A , as the longitudinal wave moves in the positive x -direction with a constant speed. The distance A is the amplitude of the wave. The y -position of the dot does not change as the wave moves through the spring. The wavelength of the wave is measured in part (d). The wavelength depends on the speed of the wave and the frequency of the driving force.

Figure 16.5 (a) This is a simple, graphical representation of a section of the stretched spring shown in (Figure)(b), representing the spring’s equilibrium position before any waves are induced on the spring. A point on the spring is marked by a blue dot. (b–g) Longitudinal waves are created by oscillating the end of the spring (not shown) back and forth along the x-axis. The longitudinal wave, with a wavelength [latex] \lambda [/latex], moves along the spring in the +x-direction with a wave speed v. For convenience, the wavelength is measured in (d). Note that the point on the spring that was marked with the blue dot moves back and forth a distance A from the equilibrium position, oscillating around the equilibrium position of the point.

Waves may be transverse, longitudinal, or a combination of the two. Examples of transverse waves are the waves on stringed instruments or surface waves on water, such as ripples moving on a pond. Sound waves in air and water are longitudinal. With sound waves, the disturbances are periodic variations in pressure that are transmitted in fluids. Fluids do not have appreciable shear strength, and for this reason, the sound waves in them are longitudinal waves. Sound in solids can have both longitudinal and transverse components, such as those in a seismic wave. Earthquakes generate seismic waves under Earth’s surface with both longitudinal and transverse components (called compressional or P-waves and shear or S-waves, respectively). The components of seismic waves have important individual characteristics—they propagate at different speeds, for example. Earthquakes also have surface waves that are similar to surface waves on water. Ocean waves also have both transverse and longitudinal components.

Wave on a String

A student takes a 30.00-m-long string and attaches one end to the wall in the physics lab. The student then holds the free end of the rope, keeping the tension constant in the rope. The student then begins to send waves down the string by moving the end of the string up and down with a frequency of 2.00 Hz. The maximum displacement of the end of the string is 20.00 cm. The first wave hits the lab wall 6.00 s after it was created. (a) What is the speed of the wave? (b) What is the period of the wave? (c) What is the wavelength of the wave?

• The speed of the wave can be derived by dividing the distance traveled by the time.
• The period of the wave is the inverse of the frequency of the driving force.
• The wavelength can be found from the speed and the period [latex] v=\lambda \text{/}T. [/latex]
• The first wave traveled 30.00 m in 6.00 s: [latex] v=\frac{30.00\,\text{m}}{6.00\,\text{s}}=5.00\frac{\text{m}}{\text{s}}. [/latex]
• The period is equal to the inverse of the frequency: [latex] T=\frac{1}{f}=\frac{1}{2.00\,{\text{s}}^{-1}}=0.50\,\text{s}. [/latex]
• The wavelength is equal to the velocity times the period: [latex] \lambda =vT=5.00\frac{\text{m}}{\text{s}}(0.50\,\text{s})=2.50\,\text{m}. [/latex]

Significance

The frequency of the wave produced by an oscillating driving force is equal to the frequency of the driving force.

Check Your Understanding

When a guitar string is plucked, the guitar string oscillates as a result of waves moving through the string. The vibrations of the string cause the air molecules to oscillate, forming sound waves. The frequency of the sound waves is equal to the frequency of the vibrating string. Is the wavelength of the sound wave always equal to the wavelength of the waves on the string?

The wavelength of the waves depends on the frequency and the velocity of the wave. The frequency of the sound wave is equal to the frequency of the wave on the string. The wavelengths of the sound waves and the waves on the string are equal only if the velocities of the waves are the same, which is not always the case. If the speed of the sound wave is different from the speed of the wave on the string, the wavelengths are different. This velocity of sound waves will be discussed in Sound .

Characteristics of a Wave

A transverse mechanical wave propagates in the positive x -direction through a spring (as shown in (Figure) (a)) with a constant wave speed, and the medium oscillates between [latex] \text{+}A [/latex] and [latex] \text{−}A [/latex] around an equilibrium position. The graph in (Figure) shows the height of the spring ( y ) versus the position ( x ), where the x -axis points in the direction of propagation. The figure shows the height of the spring versus the x -position at [latex] t=0.00\,\text{s} [/latex] as a dotted line and the wave at [latex] t=3.00\,\text{s} [/latex] as a solid line. (a) Determine the wavelength and amplitude of the wave. (b) Find the propagation velocity of the wave. (c) Calculate the period and frequency of the wave.

Figure 16.6 A transverse wave shown at two instants of time.

• The amplitude and wavelength can be determined from the graph.
• Since the velocity is constant, the velocity of the wave can be found by dividing the distance traveled by the wave by the time it took the wave to travel the distance.
• The period can be found from [latex] v=\frac{\lambda }{T} [/latex] and the frequency from [latex] f=\frac{1}{T}. [/latex]

Figure 16.7 Characteristics of the wave marked on a graph of its displacement.

• The distance the wave traveled from time [latex] t=0.00\,\text{s} [/latex] to time [latex] t=3.00\,\text{s} [/latex] can be seen in the graph. Consider the red arrow, which shows the distance the crest has moved in 3 s. The distance is [latex] 8.00\,\text{cm}-2.00\,\text{cm}=6.00\,\text{cm}. [/latex] The velocity is [latex] v=\frac{\text{Δ}x}{\text{Δ}t}=\frac{8.00\,\text{cm}-2.00\,\text{cm}}{3.00\,\text{s}-0.00\,\text{s}}=2.00\,\text{cm/s}. [/latex]
• The period is [latex] T=\frac{\lambda }{v}=\frac{8.00\,\text{cm}}{2.00\,\text{cm/s}}=4.00\,\text{s} [/latex] and the frequency is [latex] f=\frac{1}{T}=\frac{1}{4.00\,\text{s}}=0.25\,\text{Hz}. [/latex]

Note that the wavelength can be found using any two successive identical points that repeat, having the same height and slope. You should choose two points that are most convenient. The displacement can also be found using any convenient point.

The propagation velocity of a transverse or longitudinal mechanical wave may be constant as the wave disturbance moves through the medium. Consider a transverse mechanical wave: Is the velocity of the medium also constant?

• A wave is a disturbance that moves from the point of origin with a wave velocity v .
• A wave has a wavelength [latex] \lambda [/latex], which is the distance between adjacent identical parts of the wave. Wave velocity and wavelength are related to the wave’s frequency and period by [latex] v=\frac{\lambda }{T}=\lambda f. [/latex]
• Mechanical waves are disturbances that move through a medium and are governed by Newton’s laws.
• Electromagnetic waves are disturbances in the electric and magnetic fields, and do not require a medium.
• Matter waves are a central part of quantum mechanics and are associated with protons, electrons, neutrons, and other fundamental particles found in nature.
• A transverse wave has a disturbance perpendicular to the wave’s direction of propagation, whereas a longitudinal wave has a disturbance parallel to its direction of propagation.

Conceptual Questions

Give one example of a transverse wave and one example of a longitudinal wave, being careful to note the relative directions of the disturbance and wave propagation in each.

A sinusoidal transverse wave has a wavelength of 2.80 m. It takes 0.10 s for a portion of the string at a position x to move from a maximum position of [latex] y=0.03\,\text{m} [/latex] to the equilibrium position [latex] y=0. [/latex] What are the period, frequency, and wave speed of the wave?

What is the difference between propagation speed and the frequency of a mechanical wave? Does one or both affect wavelength? If so, how?

Propagation speed is the speed of the wave propagating through the medium. If the wave speed is constant, the speed can be found by [latex] v=\frac{\lambda }{T}=\lambda f. [/latex] The frequency is the number of wave that pass a point per unit time. The wavelength is directly proportional to the wave speed and inversely proportional to the frequency.

Consider a stretched spring, such as a slinky. The stretched spring can support longitudinal waves and transverse waves. How can you produce transverse waves on the spring? How can you produce longitudinal waves on the spring?

Consider a wave produced on a stretched spring by holding one end and shaking it up and down. Does the wavelength depend on the distance you move your hand up and down?

No, the distance you move your hand up and down will determine the amplitude of the wave. The wavelength will depend on the frequency you move your hand up and down, and the speed of the wave through the spring.

A sinusoidal, transverse wave is produced on a stretched spring, having a period T . Each section of the spring moves perpendicular to the direction of propagation of the wave, in simple harmonic motion with an amplitude A . Does each section oscillate with the same period as the wave or a different period? If the amplitude of the transverse wave were doubled but the period stays the same, would your answer be the same?

An electromagnetic wave, such as light, does not require a medium. Can you think of an example that would support this claim?

Storms in the South Pacific can create waves that travel all the way to the California coast, 12,000 km away. How long does it take them to travel this distance if they travel at 15.0 m/s?

Waves on a swimming pool propagate at 0.75 m/s. You splash the water at one end of the pool and observe the wave go to the opposite end, reflect, and return in 30.00 s. How far away is the other end of the pool?

[latex] 2d=vt⇒d=11.25\,\text{m} [/latex]

Wind gusts create ripples on the ocean that have a wavelength of 5.00 cm and propagate at 2.00 m/s. What is their frequency?

How many times a minute does a boat bob up and down on ocean waves that have a wavelength of 40.0 m and a propagation speed of 5.00 m/s?

Scouts at a camp shake the rope bridge they have just crossed and observe the wave crests to be 8.00 m apart. If they shake the bridge twice per second, what is the propagation speed of the waves?

What is the wavelength of the waves you create in a swimming pool if you splash your hand at a rate of 2.00 Hz and the waves propagate at a wave speed of 0.800 m/s?

[latex] v=f\lambda ⇒\lambda =0.400\,\text{m} [/latex]

What is the wavelength of an earthquake that shakes you with a frequency of 10.0 Hz and gets to another city 84.0 km away in 12.0 s?

Radio waves transmitted through empty space at the speed of light [latex] (v=c=3.00\,×\,{10}^{8}\,\text{m/s}) [/latex] by the Voyager spacecraft have a wavelength of 0.120 m. What is their frequency?

Your ear is capable of differentiating sounds that arrive at each ear just 0.34 ms apart, which is useful in determining where low frequency sound is originating from. (a) Suppose a low-frequency sound source is placed to the right of a person, whose ears are approximately 18 cm apart, and the speed of sound generated is 340 m/s. How long is the interval between when the sound arrives at the right ear and the sound arrives at the left ear? (b) Assume the same person was scuba diving and a low-frequency sound source was to the right of the scuba diver. How long is the interval between when the sound arrives at the right ear and the sound arrives at the left ear, if the speed of sound in water is 1500 m/s? (c) What is significant about the time interval of the two situations?

(a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the distance to the epicenter of the quake, geologists compare the arrival times of S- and P-waves, which travel at different speeds. If S- and P-waves travel at 4.00 and 7.20 km/s, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined? (b) Seismic waves from underground detonations of nuclear bombs can be used to locate the test site and detect violations of test bans. Discuss whether your answer to (a) implies a serious limit to such detection. (Note also that the uncertainty is greater if there is an uncertainty in the propagation speeds of the S- and P-waves.)

a. The P-waves outrun the S-waves by a speed of [latex] v=3.20\,\text{km/s;} [/latex] therefore, [latex] \text{Δ}d=0.320\,\text{km}. [/latex] b. Since the uncertainty in the distance is less than a kilometer, our answer to part (a) does not seem to limit the detection of nuclear bomb detonations. However, if the velocities are uncertain, then the uncertainty in the distance would increase and could then make it difficult to identify the source of the seismic waves.

A Girl Scout is taking a 10.00-km hike to earn a merit badge. While on the hike, she sees a cliff some distance away. She wishes to estimate the time required to walk to the cliff. She knows that the speed of sound is approximately 343 meters per second. She yells and finds that the echo returns after approximately 2.00 seconds. If she can hike 1.00 km in 10 minutes, how long would it take her to reach the cliff?

A quality assurance engineer at a frying pan company is asked to qualify a new line of nonstick-coated frying pans. The coating needs to be 1.00 mm thick. One method to test the thickness is for the engineer to pick a percentage of the pans manufactured, strip off the coating, and measure the thickness using a micrometer. This method is a destructive testing method. Instead, the engineer decides that every frying pan will be tested using a nondestructive method. An ultrasonic transducer is used that produces sound waves with a frequency of [latex] f=25\,\text{kHz}. [/latex] The sound waves are sent through the coating and are reflected by the interface between the coating and the metal pan, and the time is recorded. The wavelength of the ultrasonic waves in the coating is 0.076 m. What should be the time recorded if the coating is the correct thickness (1.00 mm)?

• OpenStax University Physics. Authored by : OpenStax CNX. Located at : https://cnx.org/contents/[email protected]:Gofkr9Oy@15 . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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Understanding Basic Traveling Waves

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After learning the basics of periodic motion, it's time to take up the study of oscillations to the next level. By the next level, I mean the dependence of the motion of the considered particle on not just the time variable, but also on the distance variable. Let's dive right into the topic by first differentiating waves.

Types of Waves

What do we mean by travelling waves, equation representing a travelling wave.

We all have heard about various kinds of of waves traveling around us. Starting from the most familiar waves of light and sound, to the complex matter waves, all of them follow a common feature, i.e. oscillation of energy.

That is what a wave is.

A wave is just the phenomenon of oscillation of energy, using various properties of a medium such as physical, electro-magnetic, etc. For example, sound waves and light waves are both the carriers of energy, but a sound wave propagates through pressure variations, whereas a light wave travels by making use of electro-magnetic phenomena, which we'll discuss shortly.

Differentiating waves on alignment of propagation with respect to oscillation:

• Longitudinal waves: The type of waves that move in such a way that the oscillation of energy is along the direction of motion of the wave is defined as a longitudinal wave . Such kind of wave can be viewed by imagining two friends, who are walking forward, one ahead of the other, such that they continue tossing a ball between each other. In this, their motion can be seen as the motion of a wave and the ball acts as the packet of energy. These waves are also known as pressure waves .
• Transverse waves: The type of waves that move in such a way that the oscillation of energy is perpendicular to the direction of the motion of the wave is defined as transverse wave. Such kind of wave can be pictured by imagining the same two friends, walking forward, but one beside another, such that they continue tossing a ball between each other. In this, their motion can be seen as the motion of a wave and the ball acts as the packet of energy.

Imagine stretching a string and fixing both its ends on two points. Now grab the mid point of the string and pull it down, before letting it go. Chances are that you'll see the mid point of the string oscillating with an amplitude, with the end points fixed at their respective positions. These kind of waves are what we call the standing waves .

Now, for the next experiment, get into a hall with your friend and call out to him. If you shout loud enough and your friend hears well, chances are that he'll hear your call. Your voice reached him by the motion of sound waves, i.e. travelling waves . Had the sound waves been stationary, your voice would have never reached him.

We all have read about the basic mathematical equation that governs the trajectory or the position of a particle in SHM, or in other words, a particle belonging to a stationary wave. It is given by \(y(t)=a\sin \omega t \), where \(a\) represents the maximum displacement of the particle from the mean position ( amplitude ), and \(\omega\) represents the angular frequency for the SHM.

Now, since a travelling wave also moves forward while changing with time, a similar equation in case of a travelling wave must definitely include a function of both the direction of propagation (let it be \(z\)) and time. So, we get: \(y\left( z,t \right) =a\sin [z,t]\), where the symbols have their usual meanings.

To find this function that will explain the oscillation of the particle, we use the basic property of linearity of the function, i.e. the function enclosed inside the \(\sin\) block must be a linear function of \(z\) and \(t,\) or else the oscillating graph would lose its shape and the wave would compress or stretch out in different locations.

So, let that be given by \(\Phi \left( z,t \right)=\alpha z+\beta t\), but since we assume the wave to be travelling towards \(z=+\infty\), \(\alpha\) and \(\beta\) must have opposite signs. Therefore,

\[\Phi \left( z,t \right)=|\alpha |z-|\beta |t.\]

Also, we already know that this function must have the dimensions of radians , so \(\beta\) has the dimensions of \(T^{-1}\) and \(\alpha\) has the dimensions of \(L^{-1}\). As it turns out, \(\alpha\) is given by a constant \(k\) that is known as the wave-number for the wave, and equals \(\frac{2\pi}{\lambda}\), where \(\lambda\) is the wavelength of the wave. On the other hand, \(\beta\) is our age old friend \(\omega\) which equals \(2\pi\nu\), where \(\nu\) is the frequency.

So, we end up with: \(y\left( z,t \right) =a\sin ({k z-\omega t}). \)

Note: If the wave travels towards \(-\infty\), the function would change to \(y\left( z,t \right) =a\sin ({k z+\omega t}) .\)

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Middle school physics - NGSS

Course: middle school physics - ngss   >   unit 4, wave properties.

• Understand: wave properties
• Apply: wave properties

Key points:

• A wave is a repeating disturbance that travels through matter or space transferring only energy.
• Below is a model of a wave.
• A wave’s crest is its highest point, and its trough is its lowest point.
• A wave’s amplitude is the maximum distance (positive or negative) a wave reaches from its rest position.
• Wavelength is the distance between the same spot on two sections of a wave.
• A wave’s frequency can be measured by how many crests (or how many troughs) pass a location in a certain amount of time.
• A wave with a larger frequency has more energy. If a wave’s frequency doubles, its energy also doubles.
• A wave’s energy is proportional to the square of its amplitude. So, if a wave’s amplitude doubles, its energy increases by four times, because 2 2 = 4 ‍   .

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13.2 Wave Properties: Speed, Amplitude, Frequency, and Period

Section learning objectives.

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

• Define amplitude, frequency, period, wavelength, and velocity of a wave
• Relate wave frequency, period, wavelength, and velocity
• Solve problems involving wave properties

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (B) investigate and analyze the characteristics of waves, including velocity, frequency, amplitude, and wavelength, and calculate using the relationship between wave speed, frequency, and wavelength;
• (D) investigate the behaviors of waves, including reflection, refraction, diffraction, interference, resonance, and the Doppler effect.

Section Key Terms

[BL] [OL] [AL] Review amplitude, period, and frequency for simple harmonic motion.

Wave Variables

In the chapter on motion in two dimensions, we defined the following variables to describe harmonic motion:

• Amplitude—maximum displacement from the equilibrium position of an object oscillating around such equilibrium position
• Frequency—number of events per unit of time
• Period—time it takes to complete one oscillation

For waves, these variables have the same basic meaning. However, it is helpful to word the definitions in a more specific way that applies directly to waves:

• Amplitude—distance between the resting position and the maximum displacement of the wave
• Frequency—number of waves passing by a specific point per second
• Period—time it takes for one wave cycle to complete

In addition to amplitude, frequency, and period, their wavelength and wave velocity also characterize waves. The wavelength λ λ is the distance between adjacent identical parts of a wave, parallel to the direction of propagation. The wave velocity v w v w is the speed at which the disturbance moves.

Tips For Success

Wave velocity is sometimes also called the propagation velocity or propagation speed because the disturbance propagates from one location to another.

Consider the periodic water wave in Figure 13.7 . Its wavelength is the distance from crest to crest or from trough to trough. The wavelength can also be thought of as the distance a wave has traveled after one complete cycle—or one period. The time for one complete up-and-down motion is the simple water wave’s period T . In the figure, the wave itself moves to the right with a wave velocity v w . Its amplitude X is the distance between the resting position and the maximum displacement—either the crest or the trough—of the wave. It is important to note that this movement of the wave is actually the disturbance moving to the right, not the water itself; otherwise, the bird would move to the right. Instead, the seagull bobs up and down in place as waves pass underneath, traveling a total distance of 2 X in one cycle. However, as mentioned in the text feature on surfing, actual ocean waves are more complex than this simplified example.

Watch Physics

Amplitude, period, frequency, and wavelength of periodic waves.

This video is a continuation of the video “Introduction to Waves” from the "Types of Waves" section. It discusses the properties of a periodic wave: amplitude, period, frequency, wavelength, and wave velocity.

The crest of a wave is sometimes also called the peak .

The Relationship between Wave Frequency, Period, Wavelength, and Velocity

Since wave frequency is the number of waves per second, and the period is essentially the number of seconds per wave, the relationship between frequency and period is

just as in the case of harmonic motion of an object. We can see from this relationship that a higher frequency means a shorter period. Recall that the unit for frequency is hertz (Hz), and that 1 Hz is one cycle—or one wave—per second.

The speed of propagation v w is the distance the wave travels in a given time, which is one wavelength in a time of one period. In equation form, it is written as

From this relationship, we see that in a medium where v w is constant, the higher the frequency, the smaller the wavelength. See Figure 13.8 .

[BL] For sound, a higher frequency corresponds to a higher pitch while a lower frequency corresponds to a lower pitch. Amplitude corresponds to the loudness of the sound.

[BL] [OL] Since sound at all frequencies has the same speed in air, a change in frequency means a change in wavelength.

[Figure Support] The same speaker is capable of reproducing both high- and low-frequency sounds. However, high frequencies have shorter wavelengths and are hence best reproduced by a speaker with a small, hard, and tight cone (tweeter), whereas lower frequencies are best reproduced by a large and soft cone (woofer).

These fundamental relationships hold true for all types of waves. As an example, for water waves, v w is the speed of a surface wave; for sound, v w is the speed of sound; and for visible light, v w is the speed of light. The amplitude X is completely independent of the speed of propagation v w and depends only on the amount of energy in the wave.

Waves in a Bowl

In this lab, you will take measurements to determine how the amplitude and the period of waves are affected by the transfer of energy from a cork dropped into the water. The cork initially has some potential energy when it is held above the water—the greater the height, the higher the potential energy. When it is dropped, such potential energy is converted to kinetic energy as the cork falls. When the cork hits the water, that energy travels through the water in waves.

• Large bowl or basin
• Cork (or ping pong ball)
• Measuring tape

Instructions

• Fill a large bowl or basin with water and wait for the water to settle so there are no ripples.
• Gently drop a cork into the middle of the bowl.
• Estimate the wavelength and the period of oscillation of the water wave that propagates away from the cork. You can estimate the period by counting the number of ripples from the center to the edge of the bowl while your partner times it. This information, combined with the bowl measurement, will give you the wavelength when the correct formula is used.
• Remove the cork from the bowl and wait for the water to settle again.
• Gently drop the cork at a height that is different from the first drop.
• Repeat Steps 3 to 5 to collect a second and third set of data, dropping the cork from different heights and recording the resulting wavelengths and periods.
• Interpret your results.
• No, only the amplitude is affected.
• Yes, the wavelength is affected.

Students can measure the bowl beforehand to help them make a better estimation of the wavelength.

Links To Physics

Geology: physics of seismic waves.

Geologists rely heavily on physics to study earthquakes since earthquakes involve several types of wave disturbances, including disturbance of Earth’s surface and pressure disturbances under the surface. Surface earthquake waves are similar to surface waves on water. The waves under Earth’s surface have both longitudinal and transverse components. The longitudinal waves in an earthquake are called pressure waves (P-waves) and the transverse waves are called shear waves (S-waves). These two types of waves propagate at different speeds, and the speed at which they travel depends on the rigidity of the medium through which they are traveling. During earthquakes, the speed of P-waves in granite is significantly higher than the speed of S-waves. Both components of earthquakes travel more slowly in less rigid materials, such as sediments. P-waves have speeds of 4 to 7 km/s, and S-waves have speeds of 2 to 5 km/s, but both are faster in more rigid materials. The P-wave gets progressively farther ahead of the S-wave as they travel through Earth’s crust. For that reason, the time difference between the P- and S-waves is used to determine the distance to their source, the epicenter of the earthquake.

We know from seismic waves produced by earthquakes that parts of the interior of Earth are liquid. Shear or transverse waves cannot travel through a liquid and are not transmitted through Earth’s core. In contrast, compression or longitudinal waves can pass through a liquid and they do go through the core.

All waves carry energy, and the energy of earthquake waves is easy to observe based on the amount of damage left behind after the ground has stopped moving. Earthquakes can shake whole cities to the ground, performing the work of thousands of wrecking balls. The amount of energy in a wave is related to its amplitude. Large-amplitude earthquakes produce large ground displacements and greater damage. As earthquake waves spread out, their amplitude decreases, so there is less damage the farther they get from the source.

Grasp Check

What is the relationship between the propagation speed, frequency, and wavelength of the S-waves in an earthquake?

• The relationship between the propagation speed, frequency, and wavelength is v w = f λ . v w = f λ .
• The relationship between the propagation speed, frequency, and wavelength is v w = λ f . v w = λ f .

Virtual Physics

Wave on a string.

In this animation, watch how a string vibrates in slow motion by choosing the Slow Motion setting. Select the No End and Manual options, and wiggle the end of the string to make waves yourself. Then switch to the Oscillate setting to generate waves automatically. Adjust the frequency and the amplitude of the oscillations to see what happens. Then experiment with adjusting the damping and the tension.

Which of the settings—amplitude, frequency, damping, or tension—changes the amplitude of the wave as it propagates? What does it do to the amplitude?

• Frequency; it decreases the amplitude of the wave as it propagates.
• Frequency; it increases the amplitude of the wave as it propagates.
• Damping; it decreases the amplitude of the wave as it propagates.
• Damping; it increases the amplitude of the wave as it propagates.

Solving Wave Problems

Worked example, calculate the velocity of wave propagation: gull in the ocean.

Calculate the wave velocity of the ocean wave in the previous figure if the distance between wave crests is 10.0 m and the time for a seagull to bob up and down is 5.00 s.

The values for the wavelength ( λ = 10.0   m ) ( λ = 10.0   m ) and the period ( T = 5.00 s) ( T = 5.00 s) are given and we are asked to find v w v w Therefore, we can use v w = λ T v w = λ T to find the wave velocity.

Enter the known values into v w = λ T v w = λ T

This slow speed seems reasonable for an ocean wave. Note that in the figure, the wave moves to the right at this speed, which is different from the varying speed at which the seagull bobs up and down.

Calculate the Period and the Wave Velocity of a Toy Spring

The woman in Figure 13.3 creates two waves every second by shaking the toy spring up and down. (a)What is the period of each wave? (b) If each wave travels 0.9 meters after one complete wave cycle, what is the velocity of wave propagation?

Strategy FOR (A)

To find the period, we solve for T = 1 f T = 1 f , given the value of the frequency ( f = 2 s − 1 ). ( f = 2 s − 1 ).

Enter the known value into T = 1 f T = 1 f

Strategy FOR (B)

Since one definition of wavelength is the distance a wave has traveled after one complete cycle—or one period—the values for the wavelength ( λ = 0.9   m ) ( λ = 0.9   m ) as well as the frequency are given. Therefore, we can use v w = f λ v w = f λ to find the wave velocity.

Enter the known values into v w = f λ v w = f λ

v w = f λ = ( 2  s −1 )(0 .9 m) = 1 .8 m/s . v w = f λ = ( 2  s −1 )(0 .9 m) = 1 .8 m/s .

We could have also used the equation v w = λ T v w = λ T to solve for the wave velocity since we already know the value of the period ( T = 0.5 s) ( T = 0.5 s) from our calculation in part (a), and we would come up with the same answer.

Practice Problems

The frequency of a wave is 10 Hz. What is its period?

• The period of the wave is 100 s.
• The period of the wave is 10 s.
• The period of the wave is 0.01 s.
• The period of the wave is 0.1 s.

What is the velocity of a wave whose wavelength is 2 m and whose frequency is 5 Hz?

Check Your Understanding

Use these questions to assess students’ achievement of the section’s Learning Objectives. If students are struggling with a specific objective, these questions will help identify such objective and direct them to the relevant content.

What is the amplitude of a wave?

• A quarter of the total height of the wave
• Half of the total height of the wave
• Two times the total height of the wave
• Four times the total height of the wave
• The wavelength is the distance between adjacent identical parts of a wave, parallel to the direction of propagation.
• The wavelength is the distance between adjacent identical parts of a wave, perpendicular to the direction of propagation.
• The wavelength is the distance between a crest and the adjacent trough of a wave, parallel to the direction of propagation.
• The wavelength is the distance between a crest and the adjacent trough of a wave, perpendicular to the direction of propagation.
• f = ( 1 T ) 2
• f = ( T ) 2

When is the wavelength directly proportional to the period of a wave?

• When the velocity of the wave is halved
• When the velocity of the wave is constant
• When the velocity of the wave is doubled
• When the velocity of the wave is tripled

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Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-physics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/physics/pages/1-introduction

• Authors: Paul Peter Urone, Roger Hinrichs
• Publisher/website: OpenStax
• Book title: Physics
• Publication date: Mar 26, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/physics/pages/1-introduction
• Section URL: https://openstax.org/books/physics/pages/13-2-wave-properties-speed-amplitude-frequency-and-period

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What is a Standing Wave Pattern?

It is however possible to have a wave confined to a given space in a medium and still produce a regular wave pattern that is readily discernible amidst the motion of the medium. For instance, if an elastic rope is held end-to-end and vibrated at just the right frequency , a wave pattern would be produced that assumes the shape of a sine wave and is seen to change over time. The wave pattern is only produced when one end of the rope is vibrated at just the right frequency. When the proper frequency is used, the interference of the incident wave and the reflected wave occur in such a manner that there are specific points along the medium that appear to be standing still. Because the observed wave pattern is characterized by points that appear to be standing still, the pattern is often called a standing wave pattern . There are other points along the medium whose displacement changes over time, but in a regular manner. These points vibrate back and forth from a positive displacement to a negative displacement; the vibrations occur at regular time intervals such that the motion of the medium is regular and repeating. A pattern is readily observable.

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Revision notes for IB Physics

Topic 4: waves.

See the guide for this topic.

4.1 – Oscillations

Simple harmonic oscillations.

Oscillations are periodic motions which center around an equilibrium position.

Simple harmonic motion (SHM) is a special type of oscillation. For example:

• The simple pendulum
• The vibration of strings in a violin
• The spring-mass system, where the mass is initially displaced to produce a periodic motion around the equilibrium position

An object undergoes SHM if it experiences a force which is proportional and opposite of the displacement from its equilibrium position.

for a pendulum

for a spring-mass system

Time period, frequency, amplitude, displacement and phase difference

Conditions for simple harmonic motion

• When the body is displaced from equilibrium, there must exist a restoring force (a force that wants to pull the body back to equilibrium).
• The magnitude of the restoring force must be proportional to the displacement of the body and acts towards the equilibrium.

4.2 – Travelling waves

Travelling waves.

A travelling wave is a continuous disturbance in a medium characterized by repeating oscillations. For example:

• A rope that is flicked up and down continuously creates a repeating disturbance similar to the shape of a sine/cosine wave.

Energy is transferred by waves.

Matter is not transferred by waves.

The direction of a wave is defined by the direction of the energy transfer.

Wavelength, frequency, period and wave speed

Wavelength, frequency, and period follow the same rules of SHM.

Wave speed can be calculated by the following equation

Transverse and longitudinal waves

The nature of electromagnetic waves.

All EM waves travel in vacuum at the same speed of 3*10^8m/s.

EM waves are transverse waves.

The nature of sound waves

The speed of sound in 20 degrees Celsius dry air is approximately 343.2m/s.

Sound waves are longitudinal waves.

4.3 – Wave characteristics

Wavefronts and rays.

Wavefronts:

• Lines joining points which vibrate in phase.
• Can be straight lines or curves.
• The distance between successive wavefronts is the wavelength of the wave.
• Lines which indicate the direction of wave propagation.
• Rays are perpendicular to wavefronts.

Amplitude and intensity

The amplitude and intensity of a wave depends on its energy.

The intensity of a wave is proportional to the square of its amplitude (I∝A^2).

See previous section with the same title.

Superposition

The principle of superposition states that the net displacement of the underlying medium for a wave is equal to the sum of the individual wave displacements.

The left shows constructive interference (superposition) where the two waves add up (e.g. 1+1=2). The right shows deconstructive interference (superposition) where the two waves cancel each other (e.g. 1+(-1)=0).

Polarization

Light is a transverse wave (polarization only occur to transverse waves).

The polarization of light refers to the orientation of the oscillation in the underlying electric field.

Light is plane polarized if the electric field oscillates in one plane.

Left shows unpolarized light and right shows polarized light.

Polarization by reflection

When light is transmitted across a boundary between two mediums with different refractive indexes, part of the light is reflected and the remaining part is refracted (for further explanation, see section 4.4).

The light reflected is partially polarized, meaning that it is a mixture of polarized light and unpolarized light.

The extent to which the reflected light is polarized depends on the angle of incidence and the refractive index of the two mediums.

The angle of incidence at which the reflected light is totally polarized is called the Brewster’s angle (ϕ) given by the equation

where n1 and n2 are the refractive indexes for their respective mediums

When the angle of incidence is equal to Brewster’s angle, the reflected ray is totally polarized and the reflected ray is perpendicular to the refracted ray.

Polarizers and Analyzers

• A polarizer is a sheet of material which polarizes light.
• When unpolarized light passes through a polarizer, its intensity is reduced by 50%.
• When polarized light passes through a polarizer, its intensity will be reduced by a factor dependent on the orientation of the polarizer. This property allows us to deduce the polarization of light by using a polarizer.
• A polarizer used for this purpose is called an analyzer.

Malus’ Law relates the incident intensity and transmitted intensity of light passing through a polarizer and an analyzer.

where I is the transmitted intensity, I0 is the initial light intensity upon the analyzer, θ is the angle between the transmission axis and the analyzer.

When light passes through an optically active substance, the plane of polarization rotates.

4.4 – Wave behaviour

Reflection and refraction.

Angle of incidence = Angle of reflection

Reflection of waves from a fixed end is inverted.

Reflection of waves from a free end is not inverted.

Refraction is the change in direction of a wave when it transmits from one medium to another.

The angle of incidence and the angle of refraction can be determined by Snell’s law given by the following formula

Fast-to-slow: towards normal; slow-to-fast: away from normal

In addition, the refractive index n1 and n2 are related by the following equation

where v1 and v2 are the speed of the waves in their respective mediums and λ1 and λ2 are the wavelength of the waves of their respective mediums

Snell’s law, critical angle and total internal reflection

See previous section (Reflection and refraction) for Snell’s law.

Diffraction through a single-slit and around objects

• Diffraction through a single-slit

Single-slit equations are not required for the standard level course.

• Diffraction around objects

Interference patterns

Maximums form at constructive interference (the maximum is shown by 1-2) and minimums form at deconstructive interference (the first minimum is shown by 3-4).

Double-slit interference

Like single-slit diffraction, double-slit diffraction occurs via the same methods of interference and has a similar diffraction pattern.

Path difference

4.5 – Standing waves

The nature of standing waves.

Standing waves (stationary) waves result from the superposition of two opposite waves which are otherwise identical.

Energy is not transferred by standing waves.

A wave hits a wall and is reflected identically opposite.

The black wave shows the wave created by the superposition of the blue and green waves.

Boundary conditions

Air particles can oscillate and create standing waves in pipes with open or closed ends.

Antinodes are positioned at open ends and nodes are positioned at closed ends.

Standing waves on a string is equivalent to that in a pipe which is closed on both ends (nodes-node).

The following table summarizes the behavior of standing waves in pipes and strings:

Nodes and antinodes

Positions along the wave which are fixed are called nodes (minimum) and those with the largest displacement are called antinodes (maximum).

For standing waves, the distance between adjacent nodes = the distance between adjacent antinodes = λ/2.

Difference between standing waves and travelling waves

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Travelling waves

Shifting the position, turning standing waves into travelling waves, another way to make waves travel, the speed of a wave on a string, for more information.

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14.1: Characteristics of a wave

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• Page ID 19461

Definition and types of waves

A traveling wave is a disturbance that travels through a medium. Consider the waves made by fans at a soccer game, as in Figure \(\PageIndex{1}\). The fans can be thought of as the medium through which the wave propagates. The elements of the medium may oscillate about an equilibrium position (the fans move a short distance up and down), but they do not travel with the wave (the fans do not move horizontally with the wave).

Consider the ripples (waves) made by a rock dropped in a pond (Figure \(\PageIndex{2}\)). The ripples travel outwards from where the rock was dropped, but the water itself does not move outwards. The individual water molecules will move in small circles about an equilibrium position, but they do not move along with the waves.

We can distinguish between two classes of waves, based on the motion of the medium through which it propagates. With transverse waves , the elements of the medium oscillate back and forth in a direction perpendicular to the motion of the wave. For example, if you attach a horizontal rope to a wall and move the other end up and down (Figure \(\PageIndex{3}\)), you can create a disturbance (a wave) that travels horizontally along the rope. The parts of the rope do not move horizontally; they only move up and down, about some equilibrium position.

With longitudinal waves , the elements of the medium oscillate back and forth in the same direction as the motion of the wave. If you clap your hands, you will create a pressure disturbance in the air that will propagate; this is what we call sound (a sound wave). The air molecules oscillate about an equilibrium position in the same direction as the wave propagates, but they do not move with the wave.

Furthermore, we can distinguish between “travelling waves”, in which a disturbance propagates through a medium, and “standing waves”, which do not transport energy through the medium (for example, a vibrating string on a violin).

Exercise \(\PageIndex{1}\)

Are the waves propagating through a slinky when you compress and elongate it (Figure \(\PageIndex{5}\)) transverse or longitudinal?

• Longitudinal

Physically, a wave can only propagate through a medium if the medium can be deformed. When a particle in the medium is disturbed from its equilibrium position, it will experience a restoring force that acts to bring it back to its equilibrium position. Often, if the displacement of the particle from the equilibrium is small, the magnitude of that force is proportional to the displacement. Thus, as we will see, we can model the propagation of waves by treating the particles in the medium as simple harmonic oscillators.

A source of energy is required in order to deform the medium and generate a wave. For example, that source of energy could be a speaker creating sound waves by pushing a membrane back and forth; speakers require energy, and are often rated by the electrical power that they convert into sound waves (e.g. a \(50\text{W}\) speaker consumes \(50\text{W}\) of electrical power to produce sound).

Description of a wave

In this chapter, we will mostly discuss how to describe sinusoidal waves; those for which the displacement of particles in the medium can be described by a sinusoidally-varying function of position. As we will see, more complicated waves can always be described as if they are the combination of multiple sine waves. We can use several quantities to describe a traveling wave, which are illustrated in Figure \(\PageIndex{7}\):

• The wavelength , \(\lambda\) , is the distance between two successive maxima (“peaks”) or minima (“troughs”) in the wave.
• The amplitude , \(A\) , is the maximal distance that a particle in the medium is displaced from its equilibrium position.
• The velocity , \(\vec v\) , is the velocity with which the disturbance propagates through the medium.
• The period , \(T\) , is the time it takes for two successive maxima (or minima) to pass through the same point in the medium.
• The frequency , \(f\) , is the inverse of the period ( \(f=1/T\) ).

The wavelength, speed, and period of the wave are related, since the amount of time that it takes for two successive maxima of the wave to pass through a given point will depend on the speed of the wave and the distance between maxima, \(\lambda\) . Since it takes a time, \(T\) , for two maxima a distance \(\lambda\) apart to pass through a given point in the medium, the speed of the wave is given by:

\[v=\frac{\lambda}{T}=\lambda f\]

Thus, of the three quantities (speed, period/frequency, and wavelength), only two are independent, as the third quantity must depend on the value of the other two. The speed of a wave depends on the properties of the medium through which the wave propagates and not on the mechanism that is generating the wave . For example, the speed of sound waves depends on the pressure, density, and temperature of the air through which they propagate, and not on what is making the sound. When a mechanism generates a wave, that mechanism usually determines the frequency of the wave (e.g. frequency with which the hand in Figure \(\PageIndex{7}\) moves up and down), the speed is determined by the medium, and the wavelength can be determined from Equation 14.1.1 .

Exercise \(\PageIndex{2}\)

What can you say about the sound emitted by a cello versus that emitted by a violin?

• The sound from the violin has a higher frequency.
• The sound from the cello has a longer wavelength.
• The sound from both instruments propagates at the same speed.
• All of the above.

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• Review Article
• Published: 22 March 2018

Cortical travelling waves: mechanisms and computational principles

• Lyle Muller 1 ,
• Frédéric Chavane 2 ,
• John Reynolds 1 &
• Terrence J. Sejnowski 1 , 3  

Nature Reviews Neuroscience volume  19 ,  pages 255–268 ( 2018 ) Cite this article

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• Dynamical systems
• Neural encoding
• Visual system

Multichannel recording technologies have revealed travelling waves of neural activity in multiple sensory, motor and cognitive systems. These waves can be spontaneously generated by recurrent circuits or evoked by external stimuli. They travel along brain networks at multiple scales, transiently modulating spiking and excitability as they pass. Here, we review recent experimental findings that have found evidence for travelling waves at single-area (mesoscopic) and whole-brain (macroscopic) scales. We place these findings in the context of the current theoretical understanding of wave generation and propagation in recurrent networks. During the large low-frequency rhythms of sleep or the relatively desynchronized state of the awake cortex, travelling waves may serve a variety of functions, from long-term memory consolidation to processing of dynamic visual stimuli. We explore new avenues for experimental and computational understanding of the role of spatiotemporal activity patterns in the cortex.

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Acknowledgements

The authors thank Z. Davis, T. Bartol, G. Pao, A. Destexhe, Y. Frégnac and C. F. Stevens for helpful discussions and J. Ogawa for helpful discussions and help with illustrations. L.M. acknowledges support from the US National Institute of Mental Health (5T32MH020002-17). F.C. acknowledges support from Agence Nationale de la Recherche (ANR) projects BalaV1 (ANR-13-BSV4-0014-02) and Trajectory (ANR-15-CE37-0011-01). J.R. acknowledges support from the Fiona and Sanjay Jha Chair in Neuroscience at the Salk Institute. T.J.S. acknowledges support from Howard Hughes Medical Institute, Swartz Foundation and the Office of Naval Research (N000141210299).

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PowerPoint slides

Powerpoint slide for fig. 1, powerpoint slide for fig. 2, powerpoint slide for fig. 3, powerpoint slide for fig. 4, powerpoint slide for fig. 5, powerpoint slide for fig. 6, powerpoint slide for table 1.

The differences in phase (an amplitude-invariant measure of position in an oscillation cycle) between two (or more) oscillations.

A disturbance that travels through a physical medium that may be water, air or a neural network.

Patterns that can result from the summation of many individual waves. Depending on the properties of the medium, the pattern resulting from these interactions can differ greatly.

A scale between microscopic and macroscopic. In neuroscience, the mesoscopic scale describes single regions (such as cortical areas or subcortical nuclei) spanning millimetres to centimetres. Cortical networks at this scale can be imaged through recently developed recording technologies.

The scale of the whole brain; traditionally recorded with extracranial techniques (electroencephalography and magnetoencephalography) and more recently recorded with intracranial methods (electrocorticography).

(EEG). A neural recording technique in which electrodes are placed on the scalp, outside the skull (extracranial), that is of great use in studying the sensory and cognitive processes of normal human subjects.

(ECoG). A recording technique in which electrodes are placed directly on the cortical surface, offering both high spatial (up to 2 millimetres or greater) and high temporal resolution.

(LFP). The electric potential recorded in the extracellular space of the cortex. The LFP is thought to reflect the synaptic currents from neurons within a few hundred micrometres around the electrode.

(MEAs). One-dimensional or two-dimensional grids of electrodes, which offer the ability to sample local field potential and spiking activity at the mesoscopic scale.

(VSDs). Fluorescent dyes applied directly to the surface of the cortex that allow the subthreshold membrane potential of neural populations to be recorded. The resulting signals are linearly related to the average membrane potential of neurons at each point in the cortex. This technique captures neural activity over a large field of view with very high spatial (up to 20 micrometres) and temporal (up to 1 millisecond) resolution.

The large, 0.1–1.0 Hz rhythm of deep non-rapid-eye-movement sleep.

Passive transmission of an electric field through biological tissue. The fields can be created from a single source of neural activity and will appear as identical, highly synchronous waveforms across electrodes; a cause of spatial smoothing (blurring) in scalp electroencephalography.

A brief ( ∼ 1 second), biphasic waveform composed of a strong negative potential followed by a positive deflection. K-Complexes occur predominantly during stage 2 non-rapid-eye-movement sleep and are driven by transitions from cortical down to up states.

Thalamocortical 11–15 Hz oscillations prevalent in stage 2 non-rapid-eye-movement sleep. These oscillatory periods have long been associated with learning and memory, including sleep-dependent consolidation of long-term memory.

A group of interconnected, repeatedly co-activated neurons whose signature spike pattern is thought to collectively represent a specific sensory stimulus or memory.

Models of emergent collective behaviour in large ensembles. In these networks, individual units are characterized by a state (or phase) between 0 and 2π. Interactions among units are typically modelled as attractive, such that units with different states tend to synchronize depending on the coupling strength of the interaction.

A state of asynchronous, highly irregular firing in spiking network models. This state exhibits the low-correlated firing that is the hallmark of cortical dynamics under general conditions of excitatory and inhibitory balance.

An extension of the neural field model of Wilson and Cowan to include the effects of neural and synaptic noise.

In rodents, the long axis of the hippocampus, running from a dorsal, medial position to a ventral, lateral position; synonymous with septotemporal axis.

Models of chemical dynamics that take into account local reactions and diffusion across space. These reactions exhibit complex dynamics, including travelling waves and emergent patterns.

A property of a system whose dynamics remain the same when time is reversed. This feature implies important mathematical properties for the system under study.

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Muller, L., Chavane, F., Reynolds, J. et al. Cortical travelling waves: mechanisms and computational principles. Nat Rev Neurosci 19 , 255–268 (2018). https://doi.org/10.1038/nrn.2018.20

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Travelling Wave Tube (TWT)

A travelling wave tube is a high power amplifier used for the amplification of microwave signals up to a wide range. It is a special type of vacuum tube that offers an operating frequency ranging between 300 MHz to 50 GHz .

Travelling wave tubes are non-resonant structures that offer continuous interaction of applied RF field with the electron beam over the entire length of the tube. Due to this reason, it provides wider operating bandwidth.

Content: Travelling Wave Tube

Basic concept.

• Construction

Need of Slow-Wave Structure

• Applications

Travelling wave tubes are abbreviated as TWT . It is majorly used in the amplification of RF signals. Basically a travelling wave tube is nothing but an elongated vacuum tube that allows the movement of electron beam inside it by the action of applied RF input.

The movement of an electron inside the tube permits the amplification of applied RF input. As it offers amplification to a wide range of frequency thus is considered more advantageous for microwave applications than other tubes.

It offers average power gain of around 60 dB . The output power lies in the range of few watts to several megawatts.

A travelling wave tube is basically of two types one is helix type and the other is coupled cavity. Here in this section, we will discuss the detailed construction and working of a helical travelling wave tube.

Construction of Travelling Wave Tube

The figure here shows the constructional structure of a TWT:

As we can see that the helical travelling wave tube consists of an electron gun and a slow-wave structure . The electron gun produces a narrow beam of the electron. A focusing plate is used that focuses the electron beam inside the tube.

A positive potential is provided to the coil (helix) with respect to the cathode terminal. While the collector is more positive than the coil (helix). In order to restrict beam spreading inside the tube. A dc magnetic field is applied between the travelling path by the help of magnets.

The signal which is needed to be amplified is provided at one of the ends of the helix, present adjacent to the electron gun. While the amplified signal is achieved at the opposite end of the helix.

In the figure, we can clearly see that attenuator is present along both the sides of the travelling wave tube. This is so because travelling wave amplifiers are high gain devices, so in case of poor load matching conditions, oscillations get build up inside the tube due to reflection.

Thus in order to restrict the generation of oscillations inside the tube attenuators are used.

Attenuators are basically formed by providing a metallic coating over the surface of the glass tube. Aquadag or Kanthal are majorly used for this.

It is to be noteworthy that a slow-wave structure is considered here, the reason is to maintain continuous interaction between the travelling wave and electron beam.

We know that the velocity of the electromagnetic wave is very much higher when compared with the phase velocity of the electron beam emitted by the electron gun.

Basically the RF wave applied at the input of TWT propagates with the speed of light (i.e., 3 * 10 8 m/s ). While the propagating velocity of the electron beam inside the tube is comparatively smaller than the velocity of RF wave.

If we try to somehow accelerate the velocity of the electron beam, then it can be accelerated only to a fraction of velocity of light. So it is better to reduce the velocity of the applied RF input in order to match the velocity of the electron beam.

Therefore, a slow-wave structure is used that causes a reduction in the phase velocity of the RF wave inside the TWT.

The slow-wave structures can be of different types like a single helix, double helix, zigzag line, corrugated, coupled-cavity or ring bar type etc.

A single helix slow-wave structure is formed by wounding a wire of element like tungsten and molybdenum in the form of a coil. The helical shape of the structure slows the velocity of the wave travelling along its axis to a fraction of about one-tenth of c.

This is so because due to the helical shape of the structure, the wave travels a much larger distance than the distance travelled by the beam inside the tube. So, in this way, the speed of wave propagation depends on the number of turns or diameter of the turns.

More specifically we can say that change in pitch can vary the speed of wave propagation inside the tube.

The equation given below shows the relation of phase velocity of the wave with the pitch of the helix:

: c = velocity of light (3 * 10 8 m/s)

V P = phase velocity in m/s

P = pitch of helix in m

d = diameter of the helix in m

Therefore, this causes continuous interaction between the RF input wave and the electron beam as the velocity of propagation of the two is not highly different. As such interaction is the basis of working of TWT thus slow-wave structures are used.

Working of Travelling Wave Tube

Till now we have discussed the complete constructional structure of TWT. Let us now understand how the signal gets amplified while travelling inside the tube.

The applied RF signal produces an electric field inside the tube. Due to the applied positive half, the moving electron beam experiences accelerative force. However, the negative half of the input applies a de-accelerative force on the moving electrons.

This is said to be velocity modulation because the electrons of the beam are experiencing different velocity inside the tube.

However, the slowly travelling wave inside the tube exhibits continuous interaction with the electron beam.

Due to the continuous interaction, the electrons moving with high velocity transfer their energy to the wave inside the tube and thus slow down. So with the rise in the amplitude of the wave, the velocity of electrons reduces and this causes bunching of electrons inside the tube.

The growing amplitude of the wave resultantly causes more bunching of electrons while reaching the end from the beginning. Thereby causing further amplification of the RF wave inside the tube.

More specifically we can say that forward progression of the field along the axis of the tube gives rise to amplification of the RF wave. Thus at the end of the tube an amplified signal is achieved.

The positive potential provided at the other end causes collection of electron bunch at the collector.

The magnetic field inside the tube restricts the spreading of the beam as the electrons possess repulsive nature.

However, as the TWT is a bidirectional device . Therefore, the reflected signal causes oscillations inside the tube. But as we have already discussed earlier that the presence of attenuators reduces the generation of oscillations due to reflected backwave.

Sometimes despite using attenuators, internal impedance terminals are used that puts less lossy effects on the forward signal.

Applications of TWT

• Travelling wave tubes are highly used in continuous wave radar systems.
• These amplifying tubes also find application in broadband receivers for RF amplification.
• TWT’s are also used to get high power output in satellite transponders.

So from the above discussion, we can conclude that no resonant structure is present in the interaction space. Thus provides amplification up to a wide bandwidth operating range.

However, the input and output coupling arrangements must be considered carefully as they limit the operating range.

Related Terms:

• Transmission Lines
• IMPATT Diode
• Backward Wave Oscillator

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'He laughs. He cries': Caleb Williams' relatability, big arm go back to high school days

WASHINGTON – Caleb Williams was halfway across the country, but that didn’t stop him from attending his senior year statistics course at Gonzaga College High School. 

“He would Zoom into my class every day from Norman, (Oklahoma),” said Terry Kernan, Gonzaga’s athletics director. “He would be in the football facility, or in his dorm room, or he’d be studying in the weight room. But he’d be there every day, just showing that commitment, where he could have easily just cashed it in and said, ‘I’m already at Oklahoma.‘ ” 

These were abnormal circumstances for a student at Gonzaga, an all-boys Jesuit private school for grades 9-12 located roughly 10 blocks from the Capitol Building. These were also abnormal times. Like millions of Americans his age, Williams completed his senior year of high school (the 2020-21 academic year) virtually as the COVID-19 pandemic curtailed in-person learning. His senior football season was canceled.

Because he could Zoom into the classroom, Williams was able to enroll early at Oklahoma. And he was still able to complete his education at Gonzaga and, ultimately, graduate. 

Doing both at the same time would have been a challenge had it not been for the pandemic, said Gonzaga’s special teams coordinator and manager of athletic communications Conrad Singh.

NFL DRAFT HUB: Latest NFL Draft mock drafts, news, live picks, grades and analysis.

“If there’s no pandemic, who knows if he wears a white tux?” said Singh, referencing the graduation attire worn by Gonzaga students. “I don’t know if that’s ever been said before. For him to be able to be at Oklahoma and here virtually, that’s unique. That’s not what Gonzaga does. If there’s no pandemic, that’s not what Gonzaga allows, so he would have been in a hard position to figure out ‘how can I be early enrolled?’”

It was a question Williams never had to answer. This preceded Williams’ lone season in Oklahoma. He subsequently transferred to Southern California, where he won the 2022 Heisman Trophy and solidified his standing as a top prospect widely expected to be taken first overall by the Chicago Bears in Thursday's NFL draft. 

Williams, Singh said, displayed a different type of mental capacity to envision the future and create situations he wants. Then he goes after it. 

“You believe in yourself and you create opportunity and choices,” Singh said. “That’s what it’s all about. And that’s what Caleb represents to a lot of people.” 

Williams returned to Gonzaga for his No. 18 jersey retirement last May. 

“He was right at home,” Singh said. “Firing the guys up, leading the fight song, he loves it here.” 

On Thursday, Williams won’t be the only Gonzaga graduate to hear his name called by NFL Commissioner Roger Goodell. Penn State left tackle Olu Fashanu, who protected Williams’ blind side for two seasons at Gonzaga, is a projected first-round pick and will be one of the first offensive tackles off the board in a loaded class at the position. 

A pair of former high-school teammates being taken in the same first round of the NFL draft isn’t unheard of. Bryant Westbrook (Lions) and Michael Booker (Falcons), for example, were teammates at El Camino High School in California and were selected six picks apart (fifth and 11th, respectively) in 1997. 

That doesn't diminish the impact the selections of Williams and Fashanu will have on Gonzaga.

“Sometimes, it’s hard for people to have perspective on how powerful or unique something is,” Gonzaga head football coach Randy Trivers told USA TODAY Sports. “This is like an eclipse. This doesn’t happen.” 

A 'relatable' QB and 'fresh mold of clay' on the line

Gonzaga beat out other schools in the D.C., Maryland, Virginia area and other prep powerhouses, such as IMG Academy in Florida, to secure Williams. The coaching staff scouted him heavily during when he was in eighth grade, current defensive coordinator and strength and conditioning coach Justin Young said. They knew he was special, Young said, but “there was just a different glow about him” upon his arrival on campus in 2017. 

“I knew he had the potential to be the starting quarterback, which is rare for a freshman for us, at any position,” Trivers said. 

The staff needed to see if he had another quality needed to be a freshman starter – the mental maturity that comes with the job. Throughout that first training camp, Williams passed each step. He digested the material in the meeting room and retained the information overnight. He proved he was tough enough during scrimmages. 

“He’s relatable in the sense that he laughs. He cries. He’s human, just like us. He loves. He can have a conversation,” said Trivers, who will be in Detroit for the draft. “Sometimes, we see these people, we don't really know them, but we imagine what they are because they do these extraordinary things.” 

Young was the offensive line coach during Williams’ freshman year and was responsible for developing a big-bodied sophomore who was still new to football: Fashanu. Now 6-foot-6 and 312 pounds, Fashanu went to Gonzaga as a basketball player who was young for his grade. He played on the freshman team before the varsity coaches brought him up the next year, Williams’ freshman campaign. Fashanu – who went on to win the 2023 Big Ten Offensive Lineman of the Year Award – didn’t play much. He spent plenty of time in the weight room with Young. Squats, explosion drills and flexibility exercises became his new language. 

“He was like a fresh mold of clay. If we got him right, bending well, kick-stepping well, he was going to be well,” Young told USA TODAY Sports. 

The Hail Mary: ‘Been riding that Caleb wave since’ 

Before being taken in the same first round, Williams and Fashanu were forever linked by Gonzaga’s 2018 Washington Catholic Athletic Conference championship – and “one of the best moments in Gonzaga history,” as Kernan put it. 

Gonzaga entered the playoffs as the No. 4 seed and upset top-seeded St. John’s on the road with Fashanu, who became the starting left tackle that season, battling an injury. In the championship against DeMatha Catholic, there were three lead changes in the final 33 seconds, the last of which came on a Hail Mary fired more than 60 yards through the air by Williams and caught by receiver John Marshall as time expired. 

The day before the championship, Gonzaga practiced that play on the same field going in the same direction.

“We were very poised to make that happen,” Singh said.

As Williams climbed the pocket as the final seconds ticked off, Fashanu kicked the pass rush out wide to give his quarterback enough space to unleash his prayer. Gonzaga defeated DeMatha, 46-43. 

“We’ve been riding the Caleb wave since he threw that Hail Mary,” Young said. 

Gonzaga lost in the WCAC semifinals in 2019, Fashanu's senior year and Williams' last season with the school due to the pandemic. More than four years later, they'll share the stage once again, this time in Detroit as NFL draftees.

“To have this No. 1 pick and another first-round pick, who played together, who are friends, who both developed under the system, who both have gone on and done great things, it would be incredible,” Kernan said. 

For the two of them to have been teammates and champions has Gonzaga “buzzing” this week, Kernan said. 

“They’re good friends to this day,” Young said. “They still talk. That’s just the brotherhood this school supplies.” 

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TCL 50 XL 5G Android smartphone hits Metro by T-Mobile: Big features, small price

• By Brian Fagioli
• Published 2 days ago

TCL Mobile is set to make waves in the budget smartphone market with the launch of the TCL 50 XL 5G, available at Metro by T-Mobile here now. As the inaugural device in the highly anticipated 50 Series, the TCL 50 XL 5G aims to bring high-end technology within reach of more consumers with its attractive price tag of just $159.

The TCL 50 XL 5G boasts a large 6.78-inch FHD+ display complemented by a smooth 120Hz refresh rate, ensuring vivid visuals and fluid motion for an immersive viewing experience. This smartphone is not just about the display; it also features dual speakers enhanced with DTS sound technology, offering a superior audio experience for both headphone users and open-air listening.

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The combination of advanced features at a low cost highlights TCL's commitment to accessibility, ensuring that more users can enjoy the benefits of 5G connectivity and multimedia capabilities without breaking the bank. The TCL 50 XL 5G stands out as a multimedia powerhouse, promising to deliver performance and value in one package.

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News & features, winter center, news / weather news, indian voters battle extreme temperatures as intense heat wave hits region.

By Helen Regan and Esha Mitra, CNN

Published Apr 26, 2024 3:50 AM PDT | Updated Apr 26, 2024 3:50 AM PDT

A taxi driver drinks water during a heat wave in Kolkata, India, on April 21. (Photo credit: Sudipta Das/NurPhoto/Getty Images via CNN Newsource)

New Delhi (CNN) —  Indian  voters are battling sweltering conditions to take part in the  world’s biggest election  as a severe heat wave hits parts of the country and authorities forecast a hotter-than-normal summer for the South Asian nation.

The India Meteorological Department (IMD) said a heat wave will affect parts of south and east India until the end of the week, including four states that are  voting on Friday .

Parts of West Bengal, Bihar, Uttar Pradesh and Karnataka are among 13 states and union territories voting in the second phase of India’s  mammoth elections , with temperatures forecast to exceed 40 degrees Celsius (104 degrees Fahrenheit) in some areas.

On Thursday, Baripada in the eastern state of Odisha hit 43.6 C (110.4 F) and Telangana’s Khammam in the south reached 43.4 C (110.1 F), according to the IMD, which warned last month that India would likely see stronger and longer heat waves this year due to above-normal temperatures.

Gandhi Ray, a farmer in his 60s from eastern Bihar state, said he lives in a small hut in the forest, and will walk to a nearby village to vote.

Temperatures above 41 C (105 F) are forecast every day until May 1 in his hometown of Banka district, according to the IMD.

“It’s important for me to vote but definitely every day this heat is getting worse and worse,” he told CNN. “I work outdoors mostly so I am used to it but as I get older it becomes harder to cope. Now my kids have taken over most of the work.”

High temperatures have raised concern this election cycle, as campaigns marked by outdoor political rallies draw thousands of people under the baking sun. The issue was underscored Wednesday, when one lawmaker  collapsed from  the heat while addressing supporters in western Maharashtra state.

The Election Commission, National Disaster Management Authority and IMD formed a task force to minimize the impact of heat waves ahead of polling days and Prime Minister Narendra Modi chaired a meeting earlier this month to review the country’s preparedness for the hot season.

The Election Commission has released guidelines for staying cool at polling stations, including drinking water and carrying an umbrella, and warned against leaving children or pets in parked cars.

And in Bihar, election officials have extended voting hours at some polling stations “in view (of the) prevailing heat wave.”

Ray said the heat isn’t going to stop him from voting on Friday.

“This is the one right we have so of course I will vote, everyone should vote for whomever they want to represent them,” he said.

“Of course it would be good if the election took place in a cooler time but whether I go to vote or not, I am still going to feel hot so that’s not going to stop me.”

Despite the heat warnings, the Election Commision  said  there are “no major concerns for heat waves” during Friday’s polling and weather forecasts indicate “normal conditions” for the constituencies voting.

Climate politics

India, the world’s most populous nation with 1.4 billion people, often experiences heat waves during the summer months of May and June. But in recent years, they have arrived earlier and become more prolonged, with scientists linking some of these longer and more intense heat waves to the climate crisis.

In 2022, a heat wave that killed 90 people across India and Pakistan was made  30 times more likely  because of climate change, the World Weather Attribution initiative found.

Last year  successive heat waves  hit India again, closing schools, damaging crops and putting pressure on energy supplies. In June alone, temperatures in some parts of the country  soared to 47 C  (116 F), killing at least 44 people and sickening hundreds with heat-related illnesses.

A man carries ice on his bicycle in Mumbai, India on Sunday, April 14. (Photo credit: Noemi Cassanelli/CNN via CNN Newsource)

The human-caused climate crisis is already threatening India’s  development goals  and putting millions of people at risk in a nation where more than 50% of the workforce is employed in agriculture, studies have found. By 2050, India will be among the places where temperatures have passed survivability limits,  according to climate experts.

But analysts say climate has not featured as a major issue this election, despite being mentioned in the election manifestos of the two main parties — the ruling  Bharatiya Janata Party  (BJP) and  the Indian National Congress.

“Climate impacts do shape voter demands — though this tends to filter through as anxieties about livelihood and continued welfare support, rather than in a neatly defined area of politics labeled ‘climate’,” said Aditya Valiathan Pillai ,  fellow and coordinator for adaptation and resilience at the New Delhi-based Sustainable Futures Collaborative,  in a recent op-ed for CNN.

“You can see it in farmers asking for loan waivers and irrigation facilities after years of drought, in urban families demanding reduced electricity prices to offset cooling bills and in calls for more penetrating social welfare.”

Regional impact

Extreme heat has already had an impact across the region this year with little respite from merciless heat and humidity for hundreds of millions of people living in areas most vulnerable to climate change.

Neighboring Bangladesh is sweltering through a heat wave this week with prolonged temperatures above 40 C in many districts and no relief during record hot nights, according to climatologist Maximiliano Herrera. The government declared a “heat alert” across the country on Thursday, in place for 72 hours.

Extreme temperatures  are also soaring across  Southeast Asia , with dozens of heatstroke deaths report by local media in Thailand, hundreds of schools closed in the Philippines, and droughts drying up rice fields and rivers in Vietnam’s Mekong Delta “rice bowl” region.

The weeks-long heat wave in Vietnam has forced three provinces to declare a state of emergency as salt seeps into fresh water sources, limiting access to drinking water for more than 70,000 households,  according  to Save the Children.

A  report released  Tuesday by the World Meteorological Organization found that Asia remained the world’s most disaster-affected region in 2023 and the region is heating up faster than the global average.

The-CNN-Wire™ & © 2024 Cable News Network, Inc., a Warner Bros. Discovery Company. All rights reserved.

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