ICSE Class 9 Physics Chapter 08 Propagation of Sound Waves

Propagation Of Sound Waves

Syllabus

(i) Nature of sound waves, Requirement of a medium for sound waves to travel; propagation and speed in different media; comparison with speed of light.

Scope - Sound propagation, terms - frequency (f), wavelength (λ), velocity (V), relation V = fλ. (simple numerical problems), effect of different factors on the speed of sound; comparison of speed of sound with speed of light, consequences of the large difference in these speeds in air, thunder and lightning.

(ii) Infrasonic, sonic, ultrasonic frequencies and their applications.

Scope - Elementary ideas and simple applications only. Difference between ultrasonic and supersonic.

Production And Propagation Of Sound Wave

8.1 Sound And Its Production From Vibrations

Everyday we hear sounds from various sources. For example, we hear sound of morning alarm, church bell, school bell, horn of a car (or bus), barking of dog, music from different instruments, etc. Although we do not see sound coming to us, but sound reaches our ears in the form of waves formed due to the vibrations of particles of the medium. The waves carry the mechanical energy of the vibrating particles which set them so as to produce a sensation of hearing in our ears. Thus

Sound is a form of energy that produces the sensation of hearing in our ears.

Sound is produced by vibrations

Sound is produced when a body vibrates. Following experiments demonstrate this fact.

Experiment (1): Stretch a string by holding one end in mouth between the teeth and the other end in one hand as shown in Fig. 8.1. Pluck it by the other hand near the middle.

It is noticed that the string starts vibrating and simultaneously a sound is heard. After some time when the string stops vibrating, no sound is heard.

Experiment (2): Take a thin wire and stretch it between the two nails about a metre apart. Place a small bit of paper as rider near the middle of the wire and pluck the wire near the rider as shown in Fig. 8.2.

It is observed that the rider flies off as the wire starts vibrating and a sound is heard. After some time when the wire stops vibrating (i.e., when the paper rider placed on the wire, does not fly off), no sound is heard.

Experiment (3): Take a tuning fork which is a rectangular rod of steel (or aluminium) bent in the U shape, with a metallic stem at the bend. Strike its one arm on a rubber pad and bring it near a table tennis ball suspended by a thread as shown in Fig. 8.3.

It is noticed that as the arm of vibrating tuning fork is brought close to the ball, it jumps to and fro and sound of the vibrating tuning fork is heard. When its arms stop vibrating, the ball becomes stationary and no sound is heard.

Experiment (4): Take a drum and beat it. The membrane of the drum vibrates which can be felt by touching it and the sound of drum is heard. As the membrane stops vibrating, no sound is heard. This shows that the vibrating drum produces sound.

Experiment (5): If the string of a sitar (or guitar) is plucked, the string starts vibrating and its sound is heard. Similarly on blowing a whistle, the air in whistle starts vibrating and a sound is heard.

From the above experiments, it is concluded that sound is produced when a body vibrates. As it stops vibrating, the sound produced by it ceases. Thus

A vibrating body is a source of sound.

Sound is a form of energy

Mechanical energy is required to start vibrations in a body producing sound. The vibrations of body are transmitted in medium in form of waves from that point to the next and so on. These waves on reaching our ears, produce vibrations in the ear drum which are perceived as sound by us. Thus, sound is a form of energy.

Teacher's Note

Every musical instrument works on the principle of vibration - from drums to guitars, all produce sound through vibrations that travel through air to reach our ears.

8.2 Sound Propagation Requires A Material Medium

Sound produced by a vibrating body travels from one place to the other through the mechanical vibrations of the medium particles in form of waves. Thus a material medium is required for the propagation of sound. This can easily be demonstrated by the following experiment.

Experiment (Bell jar experiment): Take an electric bell and an air tight glass bell jar. The electric bell is suspended inside the bell jar. The bell jar is connected to a vacuum pump as shown in Fig. 8.4. As the circuit of electric bell is completed by pressing the key, the hammer of the electric bell is seen to strike the gong repeatedly and the sound of bell is heard.

Now keeping the key pressed, air is gradually withdrawn from the jar by starting the vacuum pump. It is noticed that the loudness of sound goes on decreasing as the air is taken out from the bell jar and finally no sound is heard when the entire air from the jar has been drawn out. The hammer of electric bell is still seen striking the gong repeatedly which means that the gong is still vibrating to produce sound (as hammer strikes the gong), but it is not heard.

Explanation: When hammer of the bell hits the gong, sound is produced due to the vibrations of gong which travels through air to the wall of jar. This causes the wall of jar to vibrate due to which the air outside the jar is also set in vibration. Thus sound is heard by us. But when air has been removed from the jar, sound produced due to vibrations of gong could not travel to the wall of jar, so wall could not vibrate and no sound is heard. This clearly demonstrates that sound requires a material medium for its transmission and it cannot travel through vacuum. Thus,

A material medium is necessary for the propagation of sound from one place to another.

Requisites of the medium

The medium required for propagation of sound must possess the following three properties:

(i) The medium must be elastic so that its particles may come back to their initial positions after displacement on either side.

(ii) The medium must have inertia so that its particles may store mechanical energy.

(iii) The medium should be frictionless so that there is no loss of energy in propagation of sound through it.

Sound can propagate not only in gases, but also in solids and liquids. Some materials such as air, water, iron etc., can easily transmit sound through them from one place to another. On the other hand, blanket, thick curtains etc., absorb most of the sound incident on them and transmit or reflect only a small fraction of it.

Sound cannot travel in vacuum. On moon, there is no medium, therefore on moon, one can not hear the sound produced by the others.

Note: The light does not require any material medium for its propagation and it can therefore propagate through vacuum as well.

Teacher's Note

This is why astronauts on the moon must use radios to communicate - there is no air to carry sound, but light from their visors and equipment can still be seen.

8.3 Propagation Of Sound In A Medium

When a source of sound vibrates, it creates a periodic disturbance in the medium near it (i.e., the state of particles of medium changes). The disturbance then travels in the medium in form of waves. This can be understood by the following examples.

Example 1: Take a thin metal strip. Keeping it vertical, fix its lower end. Push its upper end to one side and then release it. As it vibrates (i.e. moves alternately to the right and left) sound is heard.

Fig. 8.5(a) shows the undisturbed or normal position of the metal strip and the air layers on the right side near the strip in their undisturbed (or normal) position.

As the strip moves to the right from a to b in Fig. 8.5(b), it pushes the particles of air in layers in front of it. So the particles of air in these layer get closer to each other i.e., air of these layers gets compressed (or compression is formed at C). The particles of the other layers while moving towards right, push and compress the layers next to them, which then compress the next layers and so on. Thus the disturbance moves forward in form of compression. The particles of the medium get displaced, but they do not move along with the compression.

As the metal strip starts returning from b to a in Fig. 8.5(c) after pushing the particles in front, the particles of air near the strip start returning back to their mean positions due to the elasticity of the medium.

When the strip moves to the left from a to c in Fig. 8.5(d), it pushes back the layers of air near it towards its left and thus produces a space of very low pressure on its right side. The air layers on the right side of the strip expand thus forming the rarefaction R.

When the strip returns from c to its normal position a in Fig. 8.5(e), it pushes the rarefaction R forward and the air layers near the strip again pass through their mean positions due to the elasticity of the medium.

In this manner, as strip moves to the right and left repeatedly, the compression and rarefaction regions are produced one after the other which carry the disturbance with it with a definite speed depending on the nature of the medium. Gradually due to friction, the strip loses its energy to the medium and the disturbance dies out.

One complete to and fro motion of the strip forms one compression and one rarefaction which together constitute one wave. This wave in which the particles of medium vibrate about their mean positions, in the direction of propagation of sound is called the longitudinal wave. Thus sound travels in air in form of longitudinal waves. Actually the longitudinal waves can be produced in solids, liquids as well as gases. At compressions, the density and pressure of the medium is maximum, while at rarefaction the density and pressure of the medium is minimum.

Example 2: In the above example, formation of waves in air could not be seen. The formation of waves can easily be seen on the surface of water. If we drop a piece of stone in the still water of a pond, we hear the sound of stone striking the water surface. Actually a disturbance is produced in water at the point where the stone strikes it. This disturbance spreads in all directions radially outwards in form of circular waves (or ripples) on the surface of water as shown in Fig. 8.6.

Now if we place a piece of cork on the water surface at some distance away from the point where the stone strikes the water, we notice that the cork does not move ahead, but it moves up and down, while the wave moves ahead. The reason is that the particles of water (or medium) start vibrating up and down at the point where the stone strikes.

These particles then transfer their energy to the other neighbouring particles and they themselves come back to their mean positions. This process continues and thus the disturbance moves ahead on the water surface in form of waves as shown in Fig. 8.7. The waves die out as soon as the energy imparted by stone gets dissipated. However, it is possible to obtain a continuously travelling wave if a periodic disturbance is produced at the point of striking the stone on the water surface.

The wave in which the particles of medium vibrate about their mean positions, in a direction perpendicular to the direction of propagation of the wave, is called the transverse wave. A transverse wave is composed of crest and trough. The position of maximum upward displacement is called crest, while the position of maximum downward displacement is called trough. The transverse waves can only be produced in solids and on the surface of liquids. They can not be produced inside liquids and in gases.

Characteristics of wave motion

(1) A wave is produced by the periodic disturbance at a point in the medium.

(2) Due to propagation of wave in a medium, the particles of medium vibrate about their mean positions (without leaving their positions) and energy is transferred with a constant speed from one place of medium to the other place.

8.4 Some Terms Related To Wave Motion

(i) Amplitude: When a wave passes through a medium, the maximum displacement of the particle of medium on either side of its mean position, is called the amplitude of wave. It is denoted by the letter a. Its S.I. unit is metre (m).

(ii) Time period: The time taken by a particle of medium to complete its one vibration is called the time period of wave. It is denoted by the letter T. Its S.I. unit is second (s).

(iii) Frequency: The number of vibrations made by a particle of medium in one second is called the frequency of wave. It is same as the number of waves passing through a point in one second. It is denoted by the letter f, n or ν (neu). Its S.I. unit is second-1 (symbol s-1) or hertz (symbol Hz).

The frequency f and time period T are related as

\[f = \frac{1}{T}\]

The frequency of a wave is equal to the frequency of vibration of its source. It is the characteristic of its source which produces the disturbance. It does not depend on the amplitude of vibration or on the nature of medium in which the wave propagates.

(iv) Wavelength: The distance travelled by the wave in one time period of vibration of particle of the medium, is called its wavelength. It is denoted by the letter λ (lambda). Its S.I. unit is metre (m). It depends on the medium in which the wave travels.

In a longitudinal wave, the distance between two consecutive compressions or between two consecutive rarefactions is equal to one wavelength, while in a transverse wave, the distance between two consecutive crests or between two consecutive troughs is equal to one wavelength.

(v) Wave velocity: The distance travelled by a wave in one second is called its wave velocity or wave speed. It is the speed with which energy is transferred from one place to the other place by wave motion. It is not the velocity of an individual particle vibrating about its mean position. It is denoted by the letter V. Its S.I. unit is metre per second (m s-1).

It may be noted that the wave velocity is constant for a given medium. It depends on the elasticity and the density of the medium. It changes when the wave passes from one medium to the other medium.

Displacement-time graph

Fig. 8.8 shows the variation of displacement with time for a particle of the medium at a given position, when a wave propagates through the medium. It is called displacement-time graph. In Fig. 8.8, the amplitude is represented by the letter a and time period is represented by the letter T. Note that each particle of the medium goes through such motion, not simultaneously, but one after another as the wave moves in the medium.

Displacement-distance graph: Fig. 8.9 shows the displacement-distance graph of a transverse wave of an instant. Here amplitude of particles of wave is shown by the letter a and wavelength is shown by the letter λ. The curve shows the displaced positions of particles of medium from their mean positions at an instant when wave propagates through the medium. It is also called snap-shot of a wave.

Teacher's Note

When you pluck a guitar string, each point on the string oscillates up and down at the same frequency, but different points reach their peak heights at different times - this is why we can draw both time and distance graphs of waves.

8.5 Relationship Between The Wavelength, Wave Velocity And Frequency

Let velocity of a wave be V, time period T, frequency f and wavelength λ. By the definition of wavelength,

Wavelength λ = Distance travelled by the wave in one time period i.e., in T second = Wave velocity × Time period = V × T

or

\[VT = \lambda\]

But \[T = \frac{1}{f}\]

Therefore, From eqn. (8.2),

\[V \times \frac{1}{f} = \lambda\]

or

\[V = f\lambda\]

Therefore,

Wave velocity = Frequency × Wavelength

In time T s, number of vibrations = 1

In 1 s, number of vibrations = 1/T = f

Teacher's Note

The relationship V = fλ is fundamental to understanding all wave motion - whether sound, light, or waves on water, this equation always holds true.

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