CBSE Class 11 Physics Sound Wave Solved Examples

Question. A man sets his watch by a whistle that is 2 km away. How much will his watch be in error: (speed of sound in air 330 m/sec)
a. 3 seconds fast
b. 3 seconds slow
c. 6 seconds fast
d. 6 seconds slow
Answer : D

Question. A stone is dropped into a lake from a tower 500 metre high. The sound of the splash will be heard by the man approximately after:
a. 11.5 seconds
b. 21 seconds
c. 10 seconds
d. 14 seconds
Answer : A

Question. A tuning fork produces waves in a medium. If the temperature of the medium changes, then which of the following will change:
a. Amplitude
b. Frequency
c. Wavelength
d. Time-period
Answer : C

Question. A man stands in front of a hillock and fires a gun. He hears an echo after 1.5 sec. The distance of the hillock from the man is: (velocity of sound in air is 330 m/s)
a. 220 m
b. 247.5 m
c. 268.5 m
d. 292.5 m
Answer : B

Question. Equation of a progressive wave is given by y = 0.2cosπ (0.04t + .02x -  π/6) 
.The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of π / 2?
a. 4 cm
b. 8 cm
c. 25 cm
d. 12.5 cm
Answer : C

Question. The displacement y (in cm) produced by a simpleharmonic wave is y = 10/π sin(2000πt - πx/17)time and maximum velocity of the particles in the mediumwill respectively be:
a. 3 10− sec and 330 m/sec
b. 4 10− sec and 20 m/sec
c. 3 10− sec and 200 m/sec
d. 2 10− sec and 2000 m/sec
Answer : C

Question. It is possible to distinguish between the transverse and longitudinal waves by studying the property of:
a. Interference
b. Diffraction
c. Reflection
d. Polarisation
Answer : D

Question. The following phenomenon cannot be observed for sound waves:
a. Refraction
b. Interference
c. Diffraction
d. Polarisation
Answer : D

Question. The speed of a wave in a certain medium is 960 m/sec. If 3600 waves pass over a certain point of the medium in 1 minute, the wavelength is:
a. 2 meters
b. 4 meters
c. 8 meters
d. 16 meters
Answer : D

Question. A simple harmonic progressive wave is represented by the equation y = 8 sin 2π (0.1x – 2t) where x and y are in cm and t is in seconds. At any instant the Phase difference between two particles separated by 2.0 cm in the xdirection is:
a. 18°
b. 36°
c. 54°
d. 72°
Answer : D

Question. The equation of a wave travelling on a string is y = 4 sin π/2 (8t - x/8) If x and y are in cm, then velocity of wave is:
a. 64 cm/sec in – x direction
b. 32 cm/sec in – x direction
c. 32 cm/sec in + x direction
d. 64 cm/sec in + x direction
Answer : D

Question. The frequency of a tunning fork is 384 per second and velocity of sound in air is 352 m/s. How far the sound has traversed while fork completes 36 vibration?
a. 3 m
b. 13 m
c. 23 m
d. 33 m
Answer : D

Question. Two waves y₁ = A₁ sin(ωt − β₁), y₂ = A₂ sin(ωt − β₂) Superimpose to form a resultant wave whose amplitude is

Answer : A

Question. Find the ratio of the speed of sound in nitrogen gas to that of helium gas, at 300 k is:
a. 1/2
b. 2/3
c. √3/5
d. 4/5
Answer : C

Question. The displacement x (in metres) of a particle performing simple harmonic motion is related to time t (in seconds) as x = 0.05 cos (4πt + π/4). The frequency of the motion will be:
a. 0.5 Hz
b. 1.0 Hz
c. 1.5 Hz
d. 2.0 Hz
Answer : D

Question. The frequency of sound wave is n and its velocity is v if the frequency is increased to 4n the velocity of the wave will be:
a. v
b. 2v
c. 4v
d. v/4
Answer : A

Question. The displacement of a particle is given by x = 3 sin (5π t)+ 4 cos (5π t ) The amplitude of particle is:
a. 3
b. 4
c. 5
d. 7
Answer : C

Question. Velocity of sound waves in air is 330 m/sec. For a particular sound in air, a path difference of 40 cm is equivalent to a phase difference of 1.6π. The frequency of this wave is:
a. 165 Hz
b. 150 Hz
c. 660 Hz
d. 330 Hz
Answer : C

Question. Find the frequency of minimum distance between compression and rarefaction of a wire. If the length of the wire is 1m and velocity of sound in air is 360 m/s:
a. 90 sec^–1
b. 180s^–1
c. 120 sec^–1
d. 360 sec^–1
Answer : A

Question. The equation of a transverse wave travelling on a rope is given by y =10 sinπ (0.01 x − 2.00 t) where y and x are in cm and t in seconds. The maximum transverse speed of a particle in the rope is about:
a. 63 cm/sec
b. 75 cm/s
c. 100 cm/sec
d. 121 cm/sec
Answer : A

Question. A wave travelling in positive X-direction with A = 0.2m has a velocity of 360 m/sec. if λ = 60m, then correct expression for the wave is:

Answer : C

Question. A wave is represented by the equation Y = 7 sin (7πt - 0.04πx + π/3) is in meters and t is in seconds.
The speed of the wave is:
a. 175 m/sec
b. 49 π m/s
c. 49/π m / s
d. 0.28 π m/s
Answer : A

Question. A wave is represented by the equation y = 0.5 sin (10t + x) m. It is a travelling wave propagating along the x direction with velocity:
a. 10 m/s
b. 20 m/s
c. 5 m/s
d. None of these
Answer : A

Question. A transverse progressive wave on a stretched string has a velocity of 10 ms–1 and a frequency of 100 Hz. The phase difference between two particles of the string which are 2.5 cm apart will be:
a. π/8
b. π/4
c. 3π/8
d. π/2
Answer : D

Question. If the ratio of amplitude of two waves is 4 : 3. Then the ratio of maximum and minimum intensity will be:
a. 16 : 18
b. 18 : 16
c. 49 : 1
d. 1 : 49
Answer : C

Question. Two tuning forks have frequencies 380 and 384 hertz respectively. When they are sounded together, they produce 4 beats. After hearing the maximum sound, how long will it take to hear the minimum sound?
a. (1/2)sec
b. (1/4)sec
c. (1/8)sec
d. (1/16)sec
Answer : C

Question. The minimum audible wavelength at room temperature is about:
a. 0.2 Å
b. 5 Å
c. 5 cm to 2 metre
d. 20 mm
Answer : D

Question. If vm is the velocity of sound in moist air, vd is the velocity of sound in dry air, under identical conditions of pressure and temperature:
a. v_m > v_d
b. v_m < v_d
c. v_m = v_d
d. v_mv_d = 1
Answer : A

Question. The minimum intensity of sound is zero at a point due to two sources of nearly equal frequencies, when:
a. Two sources are vibrating in opposite phase
b. The amplitude of two sources are equal
c. At the point of observation, the amplitudes of two
S.H.M. produced by two sources are equal and both the
S.H.M. are along the same straight line
d. Both the sources are in the same phase
Answer : C

Question. The superposition takes place between two waves of frequency f and amplitude a. The total intensity is directly proportional to:
a. a
b. 2a
c. 2 2a
d. 2 4a
Answer : D

Question. Two tuning fork A and B give 4 beats per second when sounded together. The frequency of A is 320 Hz. When some wax is added to B and it is sounded with A, 4 beats per second are again heard. The frequency of B is:
a. 312 Hz
b. 316 Hz
c. 324 Hz
d. 328 Hz
Answer : C

Question. 41 forks are so arranged that each produces 5 beat/sec when sounded with its near fork. If the frequency of last fork is double the frequency of first fork, then the frequencies of the first and last fork respectively:
a. 200, 400
b. 205, 410
c. 195, 390
d. 100, 200
Answer : A

Question. The stationary wave produced on a string is represented by the equation y = 5 cos (πx/3) sin (40πt) where x and y are in cm and t is in seconds. The distance between consecutive nodes is:
a. 5 cm
b. π cm
c. 3 cm
d. 40 cm
Answer : C

Question. On sounding tuning fork A with another tuning fork B of frequency 384 Hz, 6 beats are produced per second. After loading the prongs of A with wax and then sounding it again with B, 4 Beats are produced per second what is the frequency of the tuning fork A:
a. 388 Hz
b. 80 Hz
c. 378 Hz
d. 390 Hz
Answer : C

Question. The equation of a wave is given as y = 0.07sin (12πx − 3000πt) . Where x is in metre and t in sec, then the correct statement is:
a. λ = 1/6 m, v = 250m/s
b. a = 0.07m, v = 300m/ s
c. n =1500, v = 200m/ s
d. None
Answer : A

Question. Equation of a progressive wave is given by y = a sin π [t/2 − x/4] where t is in seconds and x is in meters. The distance through which the wave moves in 8 sec is: (in meter)
a. 8
b. 16
c. 2
d. 4
Answer : B

Question. The intensity ratio of two waves is 1 : 16. The ratio of their amplitudes is:
a. 1 : 16
b. 1 : 4
c. 4 : 1
d. 2 : 1
Answer : B

Question. A tuning fork gives 5 beats with another tuning fork of frequency 100 Hz. When the first tuning fork is loaded with wax, then the number of beats remains unchanged, then what will be the frequency of the first tuning fork:
a. 95 Hz
b. 100 Hz
c. 105 Hz
d. 110 Hz
Answer : C

Question. In stationary waves, antinodes are the points where there is
a. Minimum displacement and minimum pressure change
b. Minimum displacement and maximum pressure change
c. Maximum displacement and maximum pressure change
d. Maximum displacement and minimum pressure change
Answer : D

Question. The equation y = 0.15 sin 5x cos 300 t, describes a stationary wave. The wavelength of the stationary wave is:
a. Zero meter
b. 1.256 meter
c. 2.512 meter
d. 0.628 meter
Answer : B

Question. The equation of a stationary wave is y = 0.8 cos (πx/20)sin 200π t where x is in cm. and t is in sec. The separation between consecutive nodes will be:
a. 20 cm
b. 10 cm
c. 40 cm
d. 30 cm
Answer : A

Question. Beats are produced with the help of two sound waves on amplitude 3 and 5 units. The ratio of maximum to minimum intensity in the beats is:
a. 2 : 1
b. 5 : 3
c. 4 : 1
d. 16 : 1
Answer : D

Question. Which of the property makes difference between progressive and stationary waves?
a. Amplitude
b. Frequency
c. Propagation of energy
d. Phase of the wave
Answer : C

Question. If amplitude of waves at distance r from a point source is A, the amplitude at a distance 2r will be:
a. 2A
b. A
c. A/2
d. A/4
Answer : C

Question. Two waves are represented by y₁ = sin (ωt + π/6) and y₂ = a cosω t.What will be their resultant amplitude?
a. a
b. √2a
c. √3a
d. 2a
Answer : C

Question. A source of sound of frequency 90 vibration/sec is approaching a stationary observer with a speed equal to 1/10 the speed of sound. What will be the frequency heard by the observer:
a. 80 vibration/sec
b. 90 vibration/sec
c. 100 vibration/sec
d. 120 vibration/sec
Answer : C

Question. If two waves of same frequency and same amplitude respectively on superimposition produced a resultant disturbance of the same amplitude the wave differ in phase by:
a. π
b. 2π/3
c. π/2
d. zero
Answer : B

Question. A tuning fork of frequency 100 when sounded together with another tuning fork of unknown frequency produces 2 beats per second. On loading the tuning fork whose frequency is not known and sounded together with a tuning fork of frequency 100 produces one beat, then the requency of the other tuning fork is:
a. 102
b. 98
c. 99
d. 101
Answer : A

Question. When a tuning fork of frequency 341 is sounded with another tuning fork, six beats per second are heard. When the second tuning fork is loaded with wax and sounded with the first tuning fork, the number of beats is two per second. The natural frequency of the second tuning fork is:
a. 334
b. 339
c. 343
d. 347
Answer : D

Question. A source of sound of frequency 500 Hz is moving towards an observer with velocity 30 m/s. The speed of the sound is 330 m/s. The frequency heard by the observer will be:
a. 550 Hz
b. 458.3 Hz
c 530 Hz
d 545.5 Hz
Answer : A

Ex.1 The human ear can hear sounds from a low of 20Hz upto a maximum frequency of about 20,000 Hz. If the speed of sound in air at a temperature of 0ºC is 330 m/s, then find the wavelengths associated with these frequencies

Thus sonic sound waves have wavelengths from 16.5 mm to 16.5m.

Ex.2 If speed of sound at 0ºC is 330 m/s, then what is the speed of sound at 20ºC.
Sol. v = v0 + 0.6t
= 330 + 0.6 × 20
= 342 m/s

Ex.3 If the bulk of modulus of elasticity of water is B = 2.30 × 10⁹ N/m² and density ρ = 10³ kg/m³, then determine the speed of sound in water.

Ex.4 Calculate the temperature at which sound travels in hydrogen with the same velocity as in helium at N.T.P. The density of helium is
twice that of hydrogen.
Sol. Let θºC be the required temperature at which velocity of sound in hydrogen is same as in helium at N.T.P. (i.e.0ºC) According to Laplace's formula for the speed of sound in gases

Ex.5 A tuning fork of frequency 220Hz produces sound waves of wavelength 1.5m in air at N.T.P. Calculate the increase in wavelength, when temperature of air is 27ºC.

Ex.6 Calculate the speed of sound wave in an atmosphere of helium at 0ºC and 1atm pressure. Note that 4g of helium under STP has a volume of 22.4 litre. For He γ = 1.67.

Ex.7 At what temperature will the speed of sound in air become double of its volume at 0ºC.

Ex.8 The ratio in the densities of oxygen and nitrogen is 16 : 14. At what temperature the speed of sound will be the same which is in nitrogen at 15ºC.
Sol. If M be the molecular weight of the gas and T be the absolute temperature, then speed of sound in a gas

Ex.9 A trumpet player plays a note of frequency 400Hz with an amplitude of 8 × 10–3 mm. If the density of air is taken as 1.3 kg/m³, and the speed of sound 330 m/s, the find the intensity of the sound wave.
Sol. The intensity of sound wave is given by,
I = 2π²ρvn²a²
= 2 × (3.14)² × 1.3 × 330 × (400)² × (8 ×10^–6)²
= 2 × 9.86 × 1.3 × 330 × 16 × 64 × 10^–8
= 8.66 × 10^–2
= 0.087 W/m².

Ex.10 What is the intensity level of sound in dB for (i) threshold of hearing and (ii) threshold of pain.

Ex.11 A 5 watt source sends out waves in air at frequency 1000s^–1. Deduce the intensity at a 100 meter distance, assuming spherical distribution. If v = 350 ms^–1 and ρ = 1.3 kg/m³, deduce the displacement amplitude.
Sol. We know that intensity is given by,