CBSE Class 11 Physics Sound Wave Theory and Examples

1. INTRODUCTION

(a) Material medium is required for the propagation of sound waves.
(b) Sound waves are longitudinal in nature.
(c) Speed of sound in air at N.T.P. is 332 m/s.
(d) Sound is audiable only between 20 Hz to 20 KHz.
(e) Sound waves can not be polarised.
2. PROPAGATION OF SOUND WAVES (LONGITUDINAL WAVES)

A longitudinal wave motion is that wave motion in which individual particles of the medium execute simple harmonic motion about their mean position
along the same direction along which the wave is propagated, as shown in figure. eg.
(i) Sound waves travel through air in the form of longitudinal waves.
(ii) Vibrations of air column above the surface of water in the tube of a resonance apparatus are longitudinal.
(iii) Vibrations of air column in organ pipes are longitudinal.
A longitudinal wave travel through a medium in the form of compressions or condensations C and rarefaction (R) as shown in figure.

A compression is a region of the medium in which particles are compressed i.e. particles come closer i.e. distance between the particles becomes less than the normal distance between them. Thus there is a temporary decrease in volume and a consequent increase in density of the medium  A rarefaction is a region of the medium in which particles are rarefied i.e. particles get farther apart than what they normally are. Thus there is a temporary increase in volume and a consequent decrease in density of the medium in the region of rarefaction.

The distance between the centres of two consecutive compressions and two consecutive rarefaction is the wavelength (λ) of the wave. In above figure BD = AC = λ.
3. EQUATION OF A PROGRESSIVE SOUND WAVE

Sound wave is a longitudinal wave with regions of compression & rarefactions. The increase of pressure above its normal value may be written as,

δP = δP0 sinω (t – c/v) Where δP = increase in pressure at x position at time t δP0= maximum increase in pressure ω = 2πn where n is frequency If δP and δP0 are replaced by p & p0 then, p = p0 sinω(t – c/v)

4. VELOCITY OF SOUND IN A MEDIUM

Medium is necessary for sound propagation. These are longitudinal. In a medium, velocity of sound wave & mechanical wave depends on property of medium. It does not depends on amplitude & nature of wave.

WAVE VELOCITY IS AFFECTED BY FOLLOWING PROPERTIES OF MEDIUM :
(i) Elasticity (ii) Inertia
LAW OF NEWTON : In a medium, velocity of sound is given by

(C) VELOCITY OF SOUND IN GAS :
(I) NEWTON'S LAW : According to it, in a gaseous medium compression & rarefaction are formed slowly during wave propagation. So medium has sufficient time for energy transfer. Thus, temperature of medium remains constant. Sound wave motion is isothermal phenomenon.

5. FACTORS AFFECTING VELOCITY OF SOUND IN GASEOUS MEDIUM
(A) EFFECT OF PRESSURE AT CONSTANT TEMPERATURE : No effect, because density increases on pressure increasing.

(C) EFFECT OF HUMIDITY :
On increasing humidity, velocity of sound increases because density decreases with humidity increase. Dry air has more density than humid air.
∴ Velocity of sound in dry air is less than in humid air.

(D) EFFECT OF AMPLITUDE & FREQUENCY : No effect. In a medium, all sound waves which falls in sonic range, travels with equal velocity. Resultant velocity of wave remain same due to superposition of these waves. (Sonic velocity = 20Hz - 20000 Hz)

(E) EFFECT OF MEDIUM VELOCITY : Sound velocity changes in a dynamic medium for anobserver.

6. CHARACTERISTICS OF SOUND
There are three important characteristics of musical sound. Loudness, Pitch and Quality.

6.1 LOUDNESS
(i) Loudness of sound is a subjective term and is related to the intensity of sound. The intensity of sound at any point may be defined as the amount of sound energy passing per unit time per unit area around that point in a perpendicular direction. It is a physical quantity which is measured in Watt meter–2 in SI.
(ii) The sound waves falling on the ear drum of the observer produces the sensation of hearing. The sensation of sound which enables us to distinguish between a loud and a faint sound is called loudness. It depends upon the intensity of sound at a place and the sensitiveness of the ear of the observer situated at that place. The same sound may appear to be loud to one person and may appear faint to other. This is the reason that loudness is not entirely a physical quantity. 

Question. A motor car blowing a horn of frequency 124 vibration/sec moves with a velocity 72 km/hr towards a tall wall. The frequency of the reflected sound heard by the driver will be: (velocity of sound in air is 330 m/s)
a. 109 vibration/sec
b. 132 vibration/sec
c. 140 vibration/sec
d. 248 vibration/sec
Answer : C

Question. A man is watching two trains, one leaving and the other coming in with equal speed of 4 m/s. If they sound their whistles, each of frequency 240 Hz, the number of beats  heard by the man (velocity of sound in air = 320 m/s) will be equal to:
a. 6
b. 3
c. 0
d. 12
Answer : A

Question. Coherent sources are characterized by the same:
a. Phase and phase velocity
b. Wavelength, amplitude and phase velocity
c. Wavelength, amplitude and frequency
d. Wavelength and phase
Answer : B, C

Question. It is desired to increase the fundamental resonance frequency in a tube which is closed at one end. This can be achieved by:
a. Replacing the air in the tube by hydrogen gas
b. Increasing the length of the tube
c. Decreasing the length of the tube
d. Opening the closed end of the tube
Answer : A, B, D

Question. A wave is represented by the equation y = Asin (10πx + 15πt + π/3) where x is in meter and t is the second. The expression represents:
a. A wave traveling in the positive x-direction with a velocity 1.5 m/s
b. A wave traveling in the negative x-direction with a velocity 1.5 m/s
c. A wave traveling in the negative x-direction have a wavelength 0.2 m
d. A wave traveling in the positive x-direction have a wavelength 0.2 m
Answer : B, C

Question. A transvers sinusoidal wave of amplitude a, wavelength λ and frequency f is traveling on a stretched string. The maximum speed at any point on the string is (v/10) where v is speed of propagation of the wave. If a = 10−³ m and v = 10 ms^–1, then λ and f are given by:
a. λ = 2π ×10⁻² m
b. λ = 10⁻³ m
c. λ = 10³/ (2π) Hz
d. f = 10⁴Hz
Answer : A, C

Question. The driver of car travelling with a speed 30 meter/sec. towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is 330 m/s the frequency of reflected sound as heard by the driver is:
a. 720 Hz
b. 555.5 Hz
c. 550 Hz
d. 500 Hz
Answer : A

Question. The source of sound s is moving with a velocity 50 m/s towards a stationary observer. The observer measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? The velocity of sound in the medium is: 350 m/s
a. 750 Hz
b. 857 Hz
c. 1143 Hz
d. 1333 Hz
Answer : A

Question. A source and listener are both moving towards each other with speed v/10 where v is the speed of sound. If the frequency of the note emitted by the source is f, the frequency heard by the listener would be nearly:
a. 1.11 f
b. 1.22 f
c. f
d. 1.27 f
Answer : B

Question. A plane wave y = asin(bx + ct ) is incident on a surface.
Equation of the reflected wave is y′ = a′sin (ct − bx).
Then which of the following statements are correct:
a. The wave is incident normally on the surface
b. Reflecting surface is y-z plane
c. Medium, in which incident wave is traveling, is denser than the other medium
d. a′ cannot be greater than a.
Answer : A, B, C, D

Question. Choose the correct statements from the following:
a. Any function of the form y (x, t) = f (vt + x) represents
a not undergo any change when it is reflected form a surface
b. The velocity, wavelength and frequency of a wave do not undergo any change when it is reflected form a surface
c. When an ultrasonic wave travels form air into water, it bends towards the normal to air-water interface
d. When an ultrasonic wave travels form air into water, it bends away the normal to air-water interface
Answer : A, B, D

Question. Two waves of equal frequency f and velocity v travel in opposite directions along the same path. The wave have amplitudes A and 3A then:
a. The amplitude of the resulting wave varies with position between maxima of amplitude 4A and minima of zero amplitude
b. the distance between a maxima and adjacent minima of amplitude is v/2f
c. at point on the path the average displacement is zero
d. the position of a maxima or minima of amplitude does not change with time
Answer : C, D

Question. Which of the following statements are true?
a. For a transverse sinusoidal wave traveling along a string δy/δx = - 1/v δy/δx holds good at any instant
b. The standard one dimensional wave equation is δy/δx² = - 1/v² (δ²y/δx²)
c. A standing wave can be produced by superposing two transverse waves of equal amplitude and frequency and traveling in opposite directions
d. Superposition of waves of the same frequency and amplitude and traveling in the same direction never produces a standing wave
Answer : A, B, C

Question. Standing waves can be produced:
a. On a string clamped at both the ends
b. On a string clamped at one end and free at the other
c. When incident wave gets reflected from a wall
d. When two identical waves with a phase difference of π are moving in the same direction
Answer : A, B, C

Question. During the propagation of sound wave of frequency f, the compressions and rarefactions:
a. travel slower in water than in brass
b. in air take place such that the entropy remains constant
c. take place isothermally in all media
d. are smaller distance apart in air than in water (distance between successive compressions and rarefactions)
Answer : A, B, D

Question. A sonic source, located in a uniform medium, emits waves of frequency n. If intensity, energy density (energy per unit volume of the medium) and maximum speed of oscillations of medium particle are respectively I, E and u0 at a point then which of the following graphs are correct?

Answer : A, C, D

Question. Which of the following waves will give rise to stationary wave?
a. Asin (ωt − kx) + Asin(ωt + kx)
b. Asin (ωt + kx) − Asin(ωt + kx)
c. Asin (ωt + kx) − Asin(ωt − kx)
d. 2 Asin (ωt − kx) + Bsin 3(ωt − kx)
Answer : A, C

Question. Along the straight line joining two consecutive displacement modes in a pure stationary sound wave, at different points:
a. the SHM’s will be in different phases
b. the velocities are in phase
c. the acceleration are in phase
d. the frequencies are equal
Answer : N

Question. A transverse wave is traveling in a string. Equation of the wave:
a. Is equal to shape of the string at an instant t
b. Is general equation for displacement of the particle of the string
c. must be sinusoidal equation
d. is an equation for displacement of the particle at one end only
Answer : A

Question. Which of the following statements are correct?
a. The decrease in the speed of sound at high altitudes is due to a fall in pressure
b. The standing wave on a string under tension, fixed at its ends, does not have well-defined nodes
c. The phenomenon of beats is not observed in the case of visible light waves
d. The apparent frequency is v₁ when a source of sound approaches a stationary observer with a speed u and is v₂ when the observer approaches the same stationary source with the same speed. Then v₁ < v₂ , if u < v where v is the speed of sound
Answer : A

Question. As a wave propagates:
a. The wave intensity remains constant for a plane wave
b. The wave intensity decreases as the inverse of the distance from the source for a spherical wave
c. The wave intensity decreases as the inverse square of the distance from the source for a spherical wave
d. Total intensity of the spherical wave over the spherical surface centered at the source remains constant at all times
Answer : A, C, D

Question. A wave is traveling along a string. At an instant shape of the string is as shown in the enclosed figure. At this instant, point A is moving upwards. Which of the following statements are correct?

a. The wave is travelling to the right
b. Displacement amplitude of the wave is equal to the displacement of B at this instant
c. At this instant velocity of C is also directed upwards
d. Phase difference between A and C may be equal to π/2
Answer : B, D

Assertion and Reason

Note: Read the Assertion (A) and Reason (R) carefully to mark the correct option out of the options given below:
a. If both assertion and reason are true and the reason is the correct explanation of the assertion.
b. If both assertion and reason are true but reason is not the correct explanation of the assertion.
c. If assertion is true but reason is false.
d. If the assertion and reason both are false.
e. If assertion is false but reason is true.

73. Assertion: For small amplitudes, the motion of a simple pendulum is simple harmonic of time period T = 2π √I/g For larger amplitudes, the time period is greater than 2π√l/g
Reason: For larger amplitude, the speed of the bob is greater when it passes through the mean position.
Answer : B

Question. Assertion: The velocity of sound increases with increase in humidity.
Reason: Velocity of sound does not depend upon the medium.
Answer : C

Question. Assertion: Sound travels faster in solids than gases.
Reason: Solids possess greater density than gases.
Answer : B

Question. Assertion: The speed of sound in solids is maximum though their density is large.
Reason: The coefficient of elasticity of solid is large.
Answer : B

Question. Assertion: Sound would travel faster on a hot summer day than on a cold winter day.
Reason: Velocity of sound is directly proportional to the square of its absolute temperature.
Answer : C

Question. . Assertion: A tuning fork is made of an alloy of steel, nickel and chromium.
Reason: The alloy of steel, nickel and chromium is called elinvar.
Answer : A

Question. Assertion: Sound waves cannot propagate through vacuum but light waves can.
Reason: Sound waves cannot be polarized but light waves can be polarized.
Answer : B

Question. Assertion: Speed of wave = Wavelength/Time period
Reason: Wavelength is the distance between two nearest particles in phase.
Answer : B

Question. Assertion: The flash of lightning is seen before the sound of thunder is heard.
Reason: Speed of sound is greater than speed of light.
Answer : C

Question. Assertion: It is not possible to have interference between the waves produced by two violins.
Reason: For interference of two waves the phase difference between the waves must remain constant
Answer : B

Question. Assertion: Doppler’s effect does not occur in case of a supersonic source.
Reason: A supersonic source produced a shock wave.
Answer : A

Comprehension Based

Paragraph –I

Two waves y₁ = A cos (0.5πx – 100 πt) and y₂ = A cos (0.4πx – 92 πt) are traveling in a pipe placed along x-axis

Question. Find the number of times intensity is maximum on superposition, in time interval of 1 sec:
a. 4
b. 6
c. 8
d. 10
Answer : A

Question. The wave velocity of louder sound is:
a. 100 m/s
b. 192 m/s
c. 200 m/s
d. 96 m/s
Answer : C

Question. Find the number of times the displacement y₁ + y₂ = 0 at x = 0 in 1 sec.
a. 100
b. 46
c. 192
d. 96
Answer : D

Paragraph –II

Phenomenon of beats has most important use to find an unknown frequency of a given source. The given frequency and number of beats produced are counted. The change in beats is observed again by loading or filing one of the two sources. From the knowledge of phenom-enon of beats used to know unknown frequency, answer the following questions. Two sources A and B of known frequency v_A and unknown frequency v_B are sounded together, and n is number of beats observed. Then:

Question. On loading of A slightly number of beats decreases, then frequency of B is:
a. v_B = v_A
 b.v_B = v_A – n
c. v_B = v_A + n
d. v_B = v_A + n
Answer : B

Question. On loading of A the number of beats remain the same n, then the frequency of B is:
a. v_B = v_A
b. v_B = v_A – n
c. v_B = v_A + n
d. v_B = v_A ± n
Answer : B

Question. On loading of A the number of beats increases, the loading is reduced, then beats become the same as without loading. Then frequency of B is:
a. v_B = v_A
b. v_B = v_A – n
c. v_B = v_A + n
d. v_B = v_A ± n
Answer : B

Paragraph –III

Tow trans A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engine of train A blows a long whistle. Assume that the sound of the whistle is composed of components varying in frequency from f₁ = 800Hz to f₂ = 1120 Hz, as shown in the figure. The spread in the frequency (highest frequency lowest frequency) is thus 320 Hz. The speed of sound in still air is 340 m/s.

Question. The speed of sound of the whistle is
a. 340 m/s for passengers in A and 310 m/s for passengers in B
b. 360 m/s for passengers in A and 310 m/s for passengers in B
c. 310 m/s for passengers in A and 360 m/s for passengers in B
d. 340 m/s for passenger in both the trains
Answer : B

Question. The distribution of the sound intensity of the whistle as observed by the passengers in train A is best represented by:

Answer : A

Question. The spread of frequency as observed by the passengers in train B is:
a. 310 Hz
b. 330 Hz
c. 350 Hz
d. 290 Hz
Answer : A

Question. Waves are classified on the basis of frequency range. Column I mentions the type of waves while Column II gives the corresponding frequency range. Can you match the proper options?
      Column I                   Column II
(A) Infrasonic          1. Objects having velocity more than velocity of sound in air at 0ºC
(B) Audible              2. Frequency < 20 Hz
(C) Ultrasonics        3. Frequency > 20,000 Hz
(D) Supersonics      4. Frequency lies between 20 Hz to 20, 000 Hz
a. A → 4; B → 3; C → 2; D → 1
b. A → 2; B → 4; C → 3; D → 1
c. A → 4; B → 4; C → 1; D → 2
d. A → 3; B → 2; C → 1; D → 4
Answer : B

Integer

Question. A light pointer fixed to one prong of a tuning fork touches gently a smoked vertical plate. The fork is set vibrating and the plate is allowed to fall freely. Two complete oscillations are traced when the plate falls through 40 cm. What is the frequency (inHz) of the tuning fork?
Answer : 8

Question. The fundamental frequency of a closed organ pipe is equal to first overtone frequency of an open organ pipe. If the length of the open pipe is 36 cm, what is the length (in cm) of the closed pipe?
Answer : A

Question. A body sends waves 500 mm long through medium A and 0.25 m long in medium B. If velocity of waves in medium A is 16 m/s, what is the velocity (in m/s) of waves in medium B?
Answer : 9

Question. A source of sound S of frequency 500 Hz situated between a stationary observer O and a wall W, moves towards the wall with a speed of 2 m/s. If the velocity of sound is 332 m/s, then the number of beats per second heard by the observer is: (approximately)
Answer : 6

Question. Two identical stringed instruments have frequency 100 Hz. If tension in one of them is increased by 4% and they are sounded together then the number of beats in one second is:
Answer : 2