DC Pandey Solutions (JEE Main): Sound Waves | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


Exercises 
For JEE Main 
  Subjective Questions 
  Speed of Longitudinal Waves 
Q 1.  A person standing between two parallel hills fires a gun. He hears the first echo after 3/2 s, and a 
second echo after 5/2 s. If speed of sound is 332 m/s, calculate the distance between the hills. 
When will he hear the third echo ? 
Q 2.  Using the fact that hydrogen gas consists of diatomic molecules with M = 2 kg/K-mol.Find the 
speed of sound in hydrogen at 27° C 
Q 3.  Helium is a monoatomic gas that has a density of 0.179kg/m
3
 at a pressure of 76 cm of mercury 
and a temperature of 0° C Find the speed of compressional waves (sound) in helium at this 
temperature and pressure. 
Q 4.  (a) In a liquid with density 1300 kg / m
3
, longitudinal waves with frequency 400 Hz are found to 
have wavelength 8.00 m Calculate the bulk modulus of the liquid. 
(b) A metal bar with a length of 1.50 m has density 6400 kg/m
3
. Longitudinal sound waves take 
3.90 × 10
-4
 s to travel from one end of the bar to the other. What is Young's modulus for this metal 
? 
Q 5.  What must be the stress (F/A)in a stretched wire of a material whose Young's modulus is Y for the 
speed of longitudinal waves equal to 30 times the speed of transverse waves? 
Q 6.  A gas is a mixture of two parts by volume of hydrogen and one part by volume of nitrogen at STP. 
If the velocity of sound in hydrogen at 0° C is 1300 m/s. Find the velocity of sound in the gaseous 
mixture at 27° C. 
  Intensity and Sound Level 
Q 7.  About how many times more intense will the normal ear perceive a sound of 10
-6
 W/m
2
 than one 
of 10
-9
 W/m
2
? 
Q 8.  The explosion of a fire cracker in the air at a height of 40 m produces a 100 dB sound level at 
ground below. What is the instantaneous total radiated power? Assuming that it radiates as a point 
source. 
Q 9.  (a) What is the intensity of a 60 dB sound ? 
(b) If the sound level is 60 dB close to a speaker that has an area of 120 cm
2
. What is the acoustic 
power output of the speaker? 
Q 10.  (a) By what factor must the sound intensity be increased to increase the sound intensity level by 
13.0 dB? 
  (b) Explain why you do not need to know the original sound intensity? 
Q 11.  The speed of a certain compressional wave in air at standard temperature and pressure is 330 m/s. 
A point source of frequency 300 Hz radiates energy uniformly in all directions at the rate of 5 
watt. 
  (a) What is the intensity of the wave at a distance of 20 m from the source? 
Page 2


Exercises 
For JEE Main 
  Subjective Questions 
  Speed of Longitudinal Waves 
Q 1.  A person standing between two parallel hills fires a gun. He hears the first echo after 3/2 s, and a 
second echo after 5/2 s. If speed of sound is 332 m/s, calculate the distance between the hills. 
When will he hear the third echo ? 
Q 2.  Using the fact that hydrogen gas consists of diatomic molecules with M = 2 kg/K-mol.Find the 
speed of sound in hydrogen at 27° C 
Q 3.  Helium is a monoatomic gas that has a density of 0.179kg/m
3
 at a pressure of 76 cm of mercury 
and a temperature of 0° C Find the speed of compressional waves (sound) in helium at this 
temperature and pressure. 
Q 4.  (a) In a liquid with density 1300 kg / m
3
, longitudinal waves with frequency 400 Hz are found to 
have wavelength 8.00 m Calculate the bulk modulus of the liquid. 
(b) A metal bar with a length of 1.50 m has density 6400 kg/m
3
. Longitudinal sound waves take 
3.90 × 10
-4
 s to travel from one end of the bar to the other. What is Young's modulus for this metal 
? 
Q 5.  What must be the stress (F/A)in a stretched wire of a material whose Young's modulus is Y for the 
speed of longitudinal waves equal to 30 times the speed of transverse waves? 
Q 6.  A gas is a mixture of two parts by volume of hydrogen and one part by volume of nitrogen at STP. 
If the velocity of sound in hydrogen at 0° C is 1300 m/s. Find the velocity of sound in the gaseous 
mixture at 27° C. 
  Intensity and Sound Level 
Q 7.  About how many times more intense will the normal ear perceive a sound of 10
-6
 W/m
2
 than one 
of 10
-9
 W/m
2
? 
Q 8.  The explosion of a fire cracker in the air at a height of 40 m produces a 100 dB sound level at 
ground below. What is the instantaneous total radiated power? Assuming that it radiates as a point 
source. 
Q 9.  (a) What is the intensity of a 60 dB sound ? 
(b) If the sound level is 60 dB close to a speaker that has an area of 120 cm
2
. What is the acoustic 
power output of the speaker? 
Q 10.  (a) By what factor must the sound intensity be increased to increase the sound intensity level by 
13.0 dB? 
  (b) Explain why you do not need to know the original sound intensity? 
Q 11.  The speed of a certain compressional wave in air at standard temperature and pressure is 330 m/s. 
A point source of frequency 300 Hz radiates energy uniformly in all directions at the rate of 5 
watt. 
  (a) What is the intensity of the wave at a distance of 20 m from the source? 
  (b) What is the amplitude of the wave there? [Density of air at STP = 1.29 kg/m
3
 ] 
Q 12.  What is the amplitude of motion for the air in the path of a 60 dB, 800 Hz sound wave ? Assume 
that ?air
 
= 1.29kg/m
3
 and v = 330 m/s. 
Q 13.  A rock band gives rise to an average sound level of 102 dB at a distance of 20 m from the centre 
of the band. As an approximation, assume that the band radiates sound equally into a sphere. What 
is the sound power output of the band ? 
Q 14.  If it were possible to generate a sinusoidal 300 Hz sound wave in air that has a displacement 
amplitude of 0.200 mm. What would be the sound level of the wave ? (Assume v= 330 m/s and 
?air = 1.29 kg/m
3
) 
Q 15.  (a) A longitudinal wave propagating in a water-filled pipe has intensity 3.00 × 10
-6
 W/m
2
 and 
frequency 3400 Hz. Find the amplitude A and wavelength ? of the wave. Water has density 1000 
kg/m and bulk modulus 2.18 × 10
9
 Pa.  
  (b) If the pipe is filled with air at pressure 1.00 × 10
5
 Pa and density 1.20 kg/m
3
, what will be the 
amplitude A and wavelength ? of a longitudinal wave with the same intensity and frequency as in 
part (a)?  
  (c) In which fluid is the amplitude larger, water or air? What is the ratio of the two amplitudes? 
Why is this ratio so different from one ? Consider air as diatomic. 
Q 16.  For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz 
has a pressure amplitude of about 6.0 × 10
-5
 Pa. Calculate the corresponding intensity and sound 
intensity level at 20° C. (Assume v= 330 m/s and ?air =1.29 kg/m
3
). 
  Organ Pipes 
Q 17.  The fundamental frequency of an open pipe is 594 Hz. What is the fundamental frequency if one 
end is closed ? 
Q 18.  Find the fundamental frequency and the frequency of the first two overtones of a pipe 45.0 cm 
long.  
  (a) If the pipe is open at both ends,  (b) If the pipe is closed at one end. Use v = 344 m/s. 
Q 19.  A uniform tube of length 60 cm stands vertically with its lower end dipping into water. First two 
air column lengths above water are 15 cm and 45 cm, when the tube responds to a vibrating fork 
of frequency 500 Hz. Find the lowest frequency to which the tube will respond when it is open at 
both ends. 
Q 20.  Write the equation for the fundamental standing sound waves in a tube that is open at both ends. If 
the tube is 80 cm long and speed of the wave is 330 m/s. Represent the amplitude of the wave at 
an antinode by A. 
Q 21.  A long glass tube is held vertically, dipping into water, while a tuning fork of frequency 512 Hz is 
repeatedly struck and held over the open end. Strong resonance is obtained, when the length of the 
tube above the surface of water is 50 cm and again 84 cm, but not at any intermediate point. Find 
the speed of sound in air and next length of the air column for resonance. 
Page 3


Exercises 
For JEE Main 
  Subjective Questions 
  Speed of Longitudinal Waves 
Q 1.  A person standing between two parallel hills fires a gun. He hears the first echo after 3/2 s, and a 
second echo after 5/2 s. If speed of sound is 332 m/s, calculate the distance between the hills. 
When will he hear the third echo ? 
Q 2.  Using the fact that hydrogen gas consists of diatomic molecules with M = 2 kg/K-mol.Find the 
speed of sound in hydrogen at 27° C 
Q 3.  Helium is a monoatomic gas that has a density of 0.179kg/m
3
 at a pressure of 76 cm of mercury 
and a temperature of 0° C Find the speed of compressional waves (sound) in helium at this 
temperature and pressure. 
Q 4.  (a) In a liquid with density 1300 kg / m
3
, longitudinal waves with frequency 400 Hz are found to 
have wavelength 8.00 m Calculate the bulk modulus of the liquid. 
(b) A metal bar with a length of 1.50 m has density 6400 kg/m
3
. Longitudinal sound waves take 
3.90 × 10
-4
 s to travel from one end of the bar to the other. What is Young's modulus for this metal 
? 
Q 5.  What must be the stress (F/A)in a stretched wire of a material whose Young's modulus is Y for the 
speed of longitudinal waves equal to 30 times the speed of transverse waves? 
Q 6.  A gas is a mixture of two parts by volume of hydrogen and one part by volume of nitrogen at STP. 
If the velocity of sound in hydrogen at 0° C is 1300 m/s. Find the velocity of sound in the gaseous 
mixture at 27° C. 
  Intensity and Sound Level 
Q 7.  About how many times more intense will the normal ear perceive a sound of 10
-6
 W/m
2
 than one 
of 10
-9
 W/m
2
? 
Q 8.  The explosion of a fire cracker in the air at a height of 40 m produces a 100 dB sound level at 
ground below. What is the instantaneous total radiated power? Assuming that it radiates as a point 
source. 
Q 9.  (a) What is the intensity of a 60 dB sound ? 
(b) If the sound level is 60 dB close to a speaker that has an area of 120 cm
2
. What is the acoustic 
power output of the speaker? 
Q 10.  (a) By what factor must the sound intensity be increased to increase the sound intensity level by 
13.0 dB? 
  (b) Explain why you do not need to know the original sound intensity? 
Q 11.  The speed of a certain compressional wave in air at standard temperature and pressure is 330 m/s. 
A point source of frequency 300 Hz radiates energy uniformly in all directions at the rate of 5 
watt. 
  (a) What is the intensity of the wave at a distance of 20 m from the source? 
  (b) What is the amplitude of the wave there? [Density of air at STP = 1.29 kg/m
3
 ] 
Q 12.  What is the amplitude of motion for the air in the path of a 60 dB, 800 Hz sound wave ? Assume 
that ?air
 
= 1.29kg/m
3
 and v = 330 m/s. 
Q 13.  A rock band gives rise to an average sound level of 102 dB at a distance of 20 m from the centre 
of the band. As an approximation, assume that the band radiates sound equally into a sphere. What 
is the sound power output of the band ? 
Q 14.  If it were possible to generate a sinusoidal 300 Hz sound wave in air that has a displacement 
amplitude of 0.200 mm. What would be the sound level of the wave ? (Assume v= 330 m/s and 
?air = 1.29 kg/m
3
) 
Q 15.  (a) A longitudinal wave propagating in a water-filled pipe has intensity 3.00 × 10
-6
 W/m
2
 and 
frequency 3400 Hz. Find the amplitude A and wavelength ? of the wave. Water has density 1000 
kg/m and bulk modulus 2.18 × 10
9
 Pa.  
  (b) If the pipe is filled with air at pressure 1.00 × 10
5
 Pa and density 1.20 kg/m
3
, what will be the 
amplitude A and wavelength ? of a longitudinal wave with the same intensity and frequency as in 
part (a)?  
  (c) In which fluid is the amplitude larger, water or air? What is the ratio of the two amplitudes? 
Why is this ratio so different from one ? Consider air as diatomic. 
Q 16.  For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz 
has a pressure amplitude of about 6.0 × 10
-5
 Pa. Calculate the corresponding intensity and sound 
intensity level at 20° C. (Assume v= 330 m/s and ?air =1.29 kg/m
3
). 
  Organ Pipes 
Q 17.  The fundamental frequency of an open pipe is 594 Hz. What is the fundamental frequency if one 
end is closed ? 
Q 18.  Find the fundamental frequency and the frequency of the first two overtones of a pipe 45.0 cm 
long.  
  (a) If the pipe is open at both ends,  (b) If the pipe is closed at one end. Use v = 344 m/s. 
Q 19.  A uniform tube of length 60 cm stands vertically with its lower end dipping into water. First two 
air column lengths above water are 15 cm and 45 cm, when the tube responds to a vibrating fork 
of frequency 500 Hz. Find the lowest frequency to which the tube will respond when it is open at 
both ends. 
Q 20.  Write the equation for the fundamental standing sound waves in a tube that is open at both ends. If 
the tube is 80 cm long and speed of the wave is 330 m/s. Represent the amplitude of the wave at 
an antinode by A. 
Q 21.  A long glass tube is held vertically, dipping into water, while a tuning fork of frequency 512 Hz is 
repeatedly struck and held over the open end. Strong resonance is obtained, when the length of the 
tube above the surface of water is 50 cm and again 84 cm, but not at any intermediate point. Find 
the speed of sound in air and next length of the air column for resonance. 
Q 22.  A wire of length 40 cm which has a mass of 4 g oscillates in its second harmonic and sets the air 
column in the tube to vibrations in its fundamental mode as shown in figure. Assuming the speed 
of sound in air as 340 m/s, find the tension in the wire. 
 
Q 23.  In a resonance tube experiment to determine the speed of sound in air, a pipe of diameter 5 cm is 
used. The column in pipe resonates with a tuning fork of frequency 480 Hz when the minimum 
length of the air column is 16 cm. Find the speed of sound in air column at room temperature. 
Q 24.  The air column in a pipe closed at one end is made to vibrate in its second overtone by tuning fork 
of frequency 440 Hz. The speed of sound in air is 330 m/s. End corrections may be neglected. Let 
P0 denote the mean pressure at any point in the pipe, and ?P0 the maximum amplitude of pressure 
variation. 
  (a) Find the length L of the air column. 
  (b) What is the amplitude of pressure variation at the middle of the column ? 
  (c) What are the maximum and minimum pressure at the open end of the pipe ? 
  (d) What are the maximum and minimum pressure at the closed end of the pipe ? 
Q 25.  On a day when the speed of sound is 345 m/s, the fundamental frequency of a closed organ pipe is 
220 Hz.  
  (a) How long is this closed pipe ?  
  (b) The second overtone of this pipe has the same wavelength as the third harmonic of an open 
pipe. How long is the open pipe ? 
Q 26.  A closed organ pipe is sounded near a guitar, causing one of the strings to vibrate with large 
amplitude. We vary the tension of the string until we find the maximum amplitude. The string is 
80% as long as the closed pipe. If both the pipe and the string vibrate at their fundamental 
frequency, calculate the ratio of the wave speed on the string to the speed of sound in air. 
  Beats and Doppler Effect 
Q 27.  A police siren emits a sinusoidal wave with frequency fS = 300 Hz. The speed of sound is 340 m/s. 
(a) Find the wavelength of the waves if the siren is at rest in the air.  
  (b) If the siren is moving at 30 m/s, find the wavelength of the waves ahead of and behind the 
source. 
Q 28.  Two identical violin strings, when in tune and stretched with the same tension, have a fundamental 
frequency of 440.0 Hz. One of the string is retuned by adjusting its tension. When this is done, 1.5 
beats per second are heard when both strings are plucked simultaneously,  
Page 4


Exercises 
For JEE Main 
  Subjective Questions 
  Speed of Longitudinal Waves 
Q 1.  A person standing between two parallel hills fires a gun. He hears the first echo after 3/2 s, and a 
second echo after 5/2 s. If speed of sound is 332 m/s, calculate the distance between the hills. 
When will he hear the third echo ? 
Q 2.  Using the fact that hydrogen gas consists of diatomic molecules with M = 2 kg/K-mol.Find the 
speed of sound in hydrogen at 27° C 
Q 3.  Helium is a monoatomic gas that has a density of 0.179kg/m
3
 at a pressure of 76 cm of mercury 
and a temperature of 0° C Find the speed of compressional waves (sound) in helium at this 
temperature and pressure. 
Q 4.  (a) In a liquid with density 1300 kg / m
3
, longitudinal waves with frequency 400 Hz are found to 
have wavelength 8.00 m Calculate the bulk modulus of the liquid. 
(b) A metal bar with a length of 1.50 m has density 6400 kg/m
3
. Longitudinal sound waves take 
3.90 × 10
-4
 s to travel from one end of the bar to the other. What is Young's modulus for this metal 
? 
Q 5.  What must be the stress (F/A)in a stretched wire of a material whose Young's modulus is Y for the 
speed of longitudinal waves equal to 30 times the speed of transverse waves? 
Q 6.  A gas is a mixture of two parts by volume of hydrogen and one part by volume of nitrogen at STP. 
If the velocity of sound in hydrogen at 0° C is 1300 m/s. Find the velocity of sound in the gaseous 
mixture at 27° C. 
  Intensity and Sound Level 
Q 7.  About how many times more intense will the normal ear perceive a sound of 10
-6
 W/m
2
 than one 
of 10
-9
 W/m
2
? 
Q 8.  The explosion of a fire cracker in the air at a height of 40 m produces a 100 dB sound level at 
ground below. What is the instantaneous total radiated power? Assuming that it radiates as a point 
source. 
Q 9.  (a) What is the intensity of a 60 dB sound ? 
(b) If the sound level is 60 dB close to a speaker that has an area of 120 cm
2
. What is the acoustic 
power output of the speaker? 
Q 10.  (a) By what factor must the sound intensity be increased to increase the sound intensity level by 
13.0 dB? 
  (b) Explain why you do not need to know the original sound intensity? 
Q 11.  The speed of a certain compressional wave in air at standard temperature and pressure is 330 m/s. 
A point source of frequency 300 Hz radiates energy uniformly in all directions at the rate of 5 
watt. 
  (a) What is the intensity of the wave at a distance of 20 m from the source? 
  (b) What is the amplitude of the wave there? [Density of air at STP = 1.29 kg/m
3
 ] 
Q 12.  What is the amplitude of motion for the air in the path of a 60 dB, 800 Hz sound wave ? Assume 
that ?air
 
= 1.29kg/m
3
 and v = 330 m/s. 
Q 13.  A rock band gives rise to an average sound level of 102 dB at a distance of 20 m from the centre 
of the band. As an approximation, assume that the band radiates sound equally into a sphere. What 
is the sound power output of the band ? 
Q 14.  If it were possible to generate a sinusoidal 300 Hz sound wave in air that has a displacement 
amplitude of 0.200 mm. What would be the sound level of the wave ? (Assume v= 330 m/s and 
?air = 1.29 kg/m
3
) 
Q 15.  (a) A longitudinal wave propagating in a water-filled pipe has intensity 3.00 × 10
-6
 W/m
2
 and 
frequency 3400 Hz. Find the amplitude A and wavelength ? of the wave. Water has density 1000 
kg/m and bulk modulus 2.18 × 10
9
 Pa.  
  (b) If the pipe is filled with air at pressure 1.00 × 10
5
 Pa and density 1.20 kg/m
3
, what will be the 
amplitude A and wavelength ? of a longitudinal wave with the same intensity and frequency as in 
part (a)?  
  (c) In which fluid is the amplitude larger, water or air? What is the ratio of the two amplitudes? 
Why is this ratio so different from one ? Consider air as diatomic. 
Q 16.  For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz 
has a pressure amplitude of about 6.0 × 10
-5
 Pa. Calculate the corresponding intensity and sound 
intensity level at 20° C. (Assume v= 330 m/s and ?air =1.29 kg/m
3
). 
  Organ Pipes 
Q 17.  The fundamental frequency of an open pipe is 594 Hz. What is the fundamental frequency if one 
end is closed ? 
Q 18.  Find the fundamental frequency and the frequency of the first two overtones of a pipe 45.0 cm 
long.  
  (a) If the pipe is open at both ends,  (b) If the pipe is closed at one end. Use v = 344 m/s. 
Q 19.  A uniform tube of length 60 cm stands vertically with its lower end dipping into water. First two 
air column lengths above water are 15 cm and 45 cm, when the tube responds to a vibrating fork 
of frequency 500 Hz. Find the lowest frequency to which the tube will respond when it is open at 
both ends. 
Q 20.  Write the equation for the fundamental standing sound waves in a tube that is open at both ends. If 
the tube is 80 cm long and speed of the wave is 330 m/s. Represent the amplitude of the wave at 
an antinode by A. 
Q 21.  A long glass tube is held vertically, dipping into water, while a tuning fork of frequency 512 Hz is 
repeatedly struck and held over the open end. Strong resonance is obtained, when the length of the 
tube above the surface of water is 50 cm and again 84 cm, but not at any intermediate point. Find 
the speed of sound in air and next length of the air column for resonance. 
Q 22.  A wire of length 40 cm which has a mass of 4 g oscillates in its second harmonic and sets the air 
column in the tube to vibrations in its fundamental mode as shown in figure. Assuming the speed 
of sound in air as 340 m/s, find the tension in the wire. 
 
Q 23.  In a resonance tube experiment to determine the speed of sound in air, a pipe of diameter 5 cm is 
used. The column in pipe resonates with a tuning fork of frequency 480 Hz when the minimum 
length of the air column is 16 cm. Find the speed of sound in air column at room temperature. 
Q 24.  The air column in a pipe closed at one end is made to vibrate in its second overtone by tuning fork 
of frequency 440 Hz. The speed of sound in air is 330 m/s. End corrections may be neglected. Let 
P0 denote the mean pressure at any point in the pipe, and ?P0 the maximum amplitude of pressure 
variation. 
  (a) Find the length L of the air column. 
  (b) What is the amplitude of pressure variation at the middle of the column ? 
  (c) What are the maximum and minimum pressure at the open end of the pipe ? 
  (d) What are the maximum and minimum pressure at the closed end of the pipe ? 
Q 25.  On a day when the speed of sound is 345 m/s, the fundamental frequency of a closed organ pipe is 
220 Hz.  
  (a) How long is this closed pipe ?  
  (b) The second overtone of this pipe has the same wavelength as the third harmonic of an open 
pipe. How long is the open pipe ? 
Q 26.  A closed organ pipe is sounded near a guitar, causing one of the strings to vibrate with large 
amplitude. We vary the tension of the string until we find the maximum amplitude. The string is 
80% as long as the closed pipe. If both the pipe and the string vibrate at their fundamental 
frequency, calculate the ratio of the wave speed on the string to the speed of sound in air. 
  Beats and Doppler Effect 
Q 27.  A police siren emits a sinusoidal wave with frequency fS = 300 Hz. The speed of sound is 340 m/s. 
(a) Find the wavelength of the waves if the siren is at rest in the air.  
  (b) If the siren is moving at 30 m/s, find the wavelength of the waves ahead of and behind the 
source. 
Q 28.  Two identical violin strings, when in tune and stretched with the same tension, have a fundamental 
frequency of 440.0 Hz. One of the string is retuned by adjusting its tension. When this is done, 1.5 
beats per second are heard when both strings are plucked simultaneously,  
  (a) What are the possible fundamental frequencies of the retuned string?  
  (b) By what fractional amount was the string tension changed if it was (i) increased (ii) decreased 
? 
Q 29.  A swimming duck paddles the water with its feet once every 1.6 s, producing surface waves with 
this period. The duck is moving at constant speed in a pond where the speed of surface waves is 
0.32 m/s, and the crests of the waves ahead of the duck are spaced 0.12 mapart.  
  (a) What is the duck's speed? (b) How far apart are the crests behind the duck? 
Q 30.  A railroad train is travelling at 30.0 m/s in still air. The frequency of the note emitted by the train 
whistle is 262 Hz. What frequency is heard by a passenger on a train moving in the opposite 
direction to the first at 18.0 m/s and  
  (a) approaching the first? (b) receding from the first? Speed of sound in air= 340 m/s. 
Q 31.  A boy is walking away from a wall at a speed of 1.0 m/s in a direction at right angles to the wall. 
As he walks, he blows a whistle steadily. An observer towards whom the boy is walking hears 4.0 
beats per second. If the speed of sound is 340 m/s, what is the frequency of the whistle? 
Q 32.  The first overtone of an open organ pipe beats with the first overtone of a closed organ pipe with a 
beat frequency of 2.2 Hz. The fundamental frequency of the closed organ pipe is 110 Hz. Find the 
lengths of the pipes. Speed of sound in air v = 330 m/s. 
Q 33.  A tuning fork P of unknown frequency gives 7 beats in 2 seconds with another tuning fork Q. 
When Q runs towards a wall with a speed of 5 m/s it gives 5 beats per second with its echo. On 
loading P with wax, it gives 5 beats per second with Q. What is the frequency of P ? Assume 
speed of sound = 332 m/s. 
Q 34.  A stationary observer receives sonic oscillations from two tuning forks one of which approaches 
and the other recedes with the same velocity. As this takes place, the observer hears the beats of 
frequency f = 2.0 Hz. Find the velocity of each tuning fork if their oscillation frequency is f 0 = 680 
Hz and the velocity of sound in air is v = 340 m/s. 
  Interference in Sound 
Q 35.  Sound waves from a tuning fork A reach a point P by two separate paths ABP and ACP. When 
ACP is greater than ABP by 11.5 cm, there is silence at P. When the difference is 23 cm the sound 
becomes loudest at P and when 34.5 cm there is silence again and so on. Calculate the minimum 
frequency of the fork if the velocity of sound is taken to be 331.2 m/s. 
Q 36.  Two loudspeakers S1 and S2 each emit sounds of frequency 220 Hzuniformly in all directions. S1 
has an acoustic output of 1.2 × 10
-3
 W and S2 has 1.8 × 10
-3
 W. S1 and S2 vibrate in phase. 
Consider a point P such that S1P = 0.75 m and S2P = 3 m. How are the phases arriving at P 
related? What is the intensity at P when both S1 and S2 are on ? Speed of sound in air is 330 m/s. 
Q 37.  A source of sound emitting waves at 360 Hz is placed in front of a vertical wall, at a distance 2 m 
from it. A detector is also placed in front of the wall at the same distance from it. Find the 
minimum distance between the source and the detector for which the detector detects a maximum 
Page 5


Exercises 
For JEE Main 
  Subjective Questions 
  Speed of Longitudinal Waves 
Q 1.  A person standing between two parallel hills fires a gun. He hears the first echo after 3/2 s, and a 
second echo after 5/2 s. If speed of sound is 332 m/s, calculate the distance between the hills. 
When will he hear the third echo ? 
Q 2.  Using the fact that hydrogen gas consists of diatomic molecules with M = 2 kg/K-mol.Find the 
speed of sound in hydrogen at 27° C 
Q 3.  Helium is a monoatomic gas that has a density of 0.179kg/m
3
 at a pressure of 76 cm of mercury 
and a temperature of 0° C Find the speed of compressional waves (sound) in helium at this 
temperature and pressure. 
Q 4.  (a) In a liquid with density 1300 kg / m
3
, longitudinal waves with frequency 400 Hz are found to 
have wavelength 8.00 m Calculate the bulk modulus of the liquid. 
(b) A metal bar with a length of 1.50 m has density 6400 kg/m
3
. Longitudinal sound waves take 
3.90 × 10
-4
 s to travel from one end of the bar to the other. What is Young's modulus for this metal 
? 
Q 5.  What must be the stress (F/A)in a stretched wire of a material whose Young's modulus is Y for the 
speed of longitudinal waves equal to 30 times the speed of transverse waves? 
Q 6.  A gas is a mixture of two parts by volume of hydrogen and one part by volume of nitrogen at STP. 
If the velocity of sound in hydrogen at 0° C is 1300 m/s. Find the velocity of sound in the gaseous 
mixture at 27° C. 
  Intensity and Sound Level 
Q 7.  About how many times more intense will the normal ear perceive a sound of 10
-6
 W/m
2
 than one 
of 10
-9
 W/m
2
? 
Q 8.  The explosion of a fire cracker in the air at a height of 40 m produces a 100 dB sound level at 
ground below. What is the instantaneous total radiated power? Assuming that it radiates as a point 
source. 
Q 9.  (a) What is the intensity of a 60 dB sound ? 
(b) If the sound level is 60 dB close to a speaker that has an area of 120 cm
2
. What is the acoustic 
power output of the speaker? 
Q 10.  (a) By what factor must the sound intensity be increased to increase the sound intensity level by 
13.0 dB? 
  (b) Explain why you do not need to know the original sound intensity? 
Q 11.  The speed of a certain compressional wave in air at standard temperature and pressure is 330 m/s. 
A point source of frequency 300 Hz radiates energy uniformly in all directions at the rate of 5 
watt. 
  (a) What is the intensity of the wave at a distance of 20 m from the source? 
  (b) What is the amplitude of the wave there? [Density of air at STP = 1.29 kg/m
3
 ] 
Q 12.  What is the amplitude of motion for the air in the path of a 60 dB, 800 Hz sound wave ? Assume 
that ?air
 
= 1.29kg/m
3
 and v = 330 m/s. 
Q 13.  A rock band gives rise to an average sound level of 102 dB at a distance of 20 m from the centre 
of the band. As an approximation, assume that the band radiates sound equally into a sphere. What 
is the sound power output of the band ? 
Q 14.  If it were possible to generate a sinusoidal 300 Hz sound wave in air that has a displacement 
amplitude of 0.200 mm. What would be the sound level of the wave ? (Assume v= 330 m/s and 
?air = 1.29 kg/m
3
) 
Q 15.  (a) A longitudinal wave propagating in a water-filled pipe has intensity 3.00 × 10
-6
 W/m
2
 and 
frequency 3400 Hz. Find the amplitude A and wavelength ? of the wave. Water has density 1000 
kg/m and bulk modulus 2.18 × 10
9
 Pa.  
  (b) If the pipe is filled with air at pressure 1.00 × 10
5
 Pa and density 1.20 kg/m
3
, what will be the 
amplitude A and wavelength ? of a longitudinal wave with the same intensity and frequency as in 
part (a)?  
  (c) In which fluid is the amplitude larger, water or air? What is the ratio of the two amplitudes? 
Why is this ratio so different from one ? Consider air as diatomic. 
Q 16.  For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz 
has a pressure amplitude of about 6.0 × 10
-5
 Pa. Calculate the corresponding intensity and sound 
intensity level at 20° C. (Assume v= 330 m/s and ?air =1.29 kg/m
3
). 
  Organ Pipes 
Q 17.  The fundamental frequency of an open pipe is 594 Hz. What is the fundamental frequency if one 
end is closed ? 
Q 18.  Find the fundamental frequency and the frequency of the first two overtones of a pipe 45.0 cm 
long.  
  (a) If the pipe is open at both ends,  (b) If the pipe is closed at one end. Use v = 344 m/s. 
Q 19.  A uniform tube of length 60 cm stands vertically with its lower end dipping into water. First two 
air column lengths above water are 15 cm and 45 cm, when the tube responds to a vibrating fork 
of frequency 500 Hz. Find the lowest frequency to which the tube will respond when it is open at 
both ends. 
Q 20.  Write the equation for the fundamental standing sound waves in a tube that is open at both ends. If 
the tube is 80 cm long and speed of the wave is 330 m/s. Represent the amplitude of the wave at 
an antinode by A. 
Q 21.  A long glass tube is held vertically, dipping into water, while a tuning fork of frequency 512 Hz is 
repeatedly struck and held over the open end. Strong resonance is obtained, when the length of the 
tube above the surface of water is 50 cm and again 84 cm, but not at any intermediate point. Find 
the speed of sound in air and next length of the air column for resonance. 
Q 22.  A wire of length 40 cm which has a mass of 4 g oscillates in its second harmonic and sets the air 
column in the tube to vibrations in its fundamental mode as shown in figure. Assuming the speed 
of sound in air as 340 m/s, find the tension in the wire. 
 
Q 23.  In a resonance tube experiment to determine the speed of sound in air, a pipe of diameter 5 cm is 
used. The column in pipe resonates with a tuning fork of frequency 480 Hz when the minimum 
length of the air column is 16 cm. Find the speed of sound in air column at room temperature. 
Q 24.  The air column in a pipe closed at one end is made to vibrate in its second overtone by tuning fork 
of frequency 440 Hz. The speed of sound in air is 330 m/s. End corrections may be neglected. Let 
P0 denote the mean pressure at any point in the pipe, and ?P0 the maximum amplitude of pressure 
variation. 
  (a) Find the length L of the air column. 
  (b) What is the amplitude of pressure variation at the middle of the column ? 
  (c) What are the maximum and minimum pressure at the open end of the pipe ? 
  (d) What are the maximum and minimum pressure at the closed end of the pipe ? 
Q 25.  On a day when the speed of sound is 345 m/s, the fundamental frequency of a closed organ pipe is 
220 Hz.  
  (a) How long is this closed pipe ?  
  (b) The second overtone of this pipe has the same wavelength as the third harmonic of an open 
pipe. How long is the open pipe ? 
Q 26.  A closed organ pipe is sounded near a guitar, causing one of the strings to vibrate with large 
amplitude. We vary the tension of the string until we find the maximum amplitude. The string is 
80% as long as the closed pipe. If both the pipe and the string vibrate at their fundamental 
frequency, calculate the ratio of the wave speed on the string to the speed of sound in air. 
  Beats and Doppler Effect 
Q 27.  A police siren emits a sinusoidal wave with frequency fS = 300 Hz. The speed of sound is 340 m/s. 
(a) Find the wavelength of the waves if the siren is at rest in the air.  
  (b) If the siren is moving at 30 m/s, find the wavelength of the waves ahead of and behind the 
source. 
Q 28.  Two identical violin strings, when in tune and stretched with the same tension, have a fundamental 
frequency of 440.0 Hz. One of the string is retuned by adjusting its tension. When this is done, 1.5 
beats per second are heard when both strings are plucked simultaneously,  
  (a) What are the possible fundamental frequencies of the retuned string?  
  (b) By what fractional amount was the string tension changed if it was (i) increased (ii) decreased 
? 
Q 29.  A swimming duck paddles the water with its feet once every 1.6 s, producing surface waves with 
this period. The duck is moving at constant speed in a pond where the speed of surface waves is 
0.32 m/s, and the crests of the waves ahead of the duck are spaced 0.12 mapart.  
  (a) What is the duck's speed? (b) How far apart are the crests behind the duck? 
Q 30.  A railroad train is travelling at 30.0 m/s in still air. The frequency of the note emitted by the train 
whistle is 262 Hz. What frequency is heard by a passenger on a train moving in the opposite 
direction to the first at 18.0 m/s and  
  (a) approaching the first? (b) receding from the first? Speed of sound in air= 340 m/s. 
Q 31.  A boy is walking away from a wall at a speed of 1.0 m/s in a direction at right angles to the wall. 
As he walks, he blows a whistle steadily. An observer towards whom the boy is walking hears 4.0 
beats per second. If the speed of sound is 340 m/s, what is the frequency of the whistle? 
Q 32.  The first overtone of an open organ pipe beats with the first overtone of a closed organ pipe with a 
beat frequency of 2.2 Hz. The fundamental frequency of the closed organ pipe is 110 Hz. Find the 
lengths of the pipes. Speed of sound in air v = 330 m/s. 
Q 33.  A tuning fork P of unknown frequency gives 7 beats in 2 seconds with another tuning fork Q. 
When Q runs towards a wall with a speed of 5 m/s it gives 5 beats per second with its echo. On 
loading P with wax, it gives 5 beats per second with Q. What is the frequency of P ? Assume 
speed of sound = 332 m/s. 
Q 34.  A stationary observer receives sonic oscillations from two tuning forks one of which approaches 
and the other recedes with the same velocity. As this takes place, the observer hears the beats of 
frequency f = 2.0 Hz. Find the velocity of each tuning fork if their oscillation frequency is f 0 = 680 
Hz and the velocity of sound in air is v = 340 m/s. 
  Interference in Sound 
Q 35.  Sound waves from a tuning fork A reach a point P by two separate paths ABP and ACP. When 
ACP is greater than ABP by 11.5 cm, there is silence at P. When the difference is 23 cm the sound 
becomes loudest at P and when 34.5 cm there is silence again and so on. Calculate the minimum 
frequency of the fork if the velocity of sound is taken to be 331.2 m/s. 
Q 36.  Two loudspeakers S1 and S2 each emit sounds of frequency 220 Hzuniformly in all directions. S1 
has an acoustic output of 1.2 × 10
-3
 W and S2 has 1.8 × 10
-3
 W. S1 and S2 vibrate in phase. 
Consider a point P such that S1P = 0.75 m and S2P = 3 m. How are the phases arriving at P 
related? What is the intensity at P when both S1 and S2 are on ? Speed of sound in air is 330 m/s. 
Q 37.  A source of sound emitting waves at 360 Hz is placed in front of a vertical wall, at a distance 2 m 
from it. A detector is also placed in front of the wall at the same distance from it. Find the 
minimum distance between the source and the detector for which the detector detects a maximum 
of sound. Take speed of sound in air = 360 m/s. Assume that there is no phase change in reflected 
wave. 
 
Solutions 
1.  
   
   
   = 415m 
  ?   Total distance = d1 + d2 = 664 m Next echo he will hear after time 
    
   = 4 s 
2.   
3.  
     
   
4.  (a) 
   
   = (1300) (400 × 8)
2 
= 1.33 × 10
10
N/m
2
 
  (b)