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

 Page 1


Introductory Exercise 16.1
Q1: Calculate the bulk modulus of air from the following data for a sound
wave of wavelength 35 cm travelling in air. The pressure at a point varies
between (10 ± 14) Pa and the particles of the air vibrate in SHM of
amplitude 5.5 × 10 m.
Sol: 
Q2: Find the minimum and maximum wavelengths of sound in water that is
in the audible range for an average human ear. Speed of sound in water is
1450 m/s.
Sol: (a) For minimum wavelength n = 20 KHz
Q3: A typical loud sound wave with a frequency of 1 kHz has a pressure
amplitude of about 10 Pa (a) At t = 0, the pressure is a maximum at some
point x . What is the displacement at that point at t = 0?
5
-6
1
Page 2


Introductory Exercise 16.1
Q1: Calculate the bulk modulus of air from the following data for a sound
wave of wavelength 35 cm travelling in air. The pressure at a point varies
between (10 ± 14) Pa and the particles of the air vibrate in SHM of
amplitude 5.5 × 10 m.
Sol: 
Q2: Find the minimum and maximum wavelengths of sound in water that is
in the audible range for an average human ear. Speed of sound in water is
1450 m/s.
Sol: (a) For minimum wavelength n = 20 KHz
Q3: A typical loud sound wave with a frequency of 1 kHz has a pressure
amplitude of about 10 Pa (a) At t = 0, the pressure is a maximum at some
point x . What is the displacement at that point at t = 0?
5
-6
1
(b) What is the maximum value of the displacement at any time and place ?
Take the density of air to be 1.29 kg/m and speed of sound in air is 340
m/s.
Sol: (a) Displacement is zero when pressure is maximum.
Q4:  The pressure variation in a sound wave in air is given by
?P = 12 sin(8.18x - 2700t +p/4) N/m
Find the displacement amplitude. Density of air = 1.29 kg/m .
Sol: In the above problem, we have found that
Now substituting the value, we have
 
Introductory Exercise 16.2
Q1: Calculate the temperature at which the velocity of sound in air is
double its velocity at 0°C.
Sol: Speed of velocity in air is, v ? vT 
3
2
3
Page 3


Introductory Exercise 16.1
Q1: Calculate the bulk modulus of air from the following data for a sound
wave of wavelength 35 cm travelling in air. The pressure at a point varies
between (10 ± 14) Pa and the particles of the air vibrate in SHM of
amplitude 5.5 × 10 m.
Sol: 
Q2: Find the minimum and maximum wavelengths of sound in water that is
in the audible range for an average human ear. Speed of sound in water is
1450 m/s.
Sol: (a) For minimum wavelength n = 20 KHz
Q3: A typical loud sound wave with a frequency of 1 kHz has a pressure
amplitude of about 10 Pa (a) At t = 0, the pressure is a maximum at some
point x . What is the displacement at that point at t = 0?
5
-6
1
(b) What is the maximum value of the displacement at any time and place ?
Take the density of air to be 1.29 kg/m and speed of sound in air is 340
m/s.
Sol: (a) Displacement is zero when pressure is maximum.
Q4:  The pressure variation in a sound wave in air is given by
?P = 12 sin(8.18x - 2700t +p/4) N/m
Find the displacement amplitude. Density of air = 1.29 kg/m .
Sol: In the above problem, we have found that
Now substituting the value, we have
 
Introductory Exercise 16.2
Q1: Calculate the temperature at which the velocity of sound in air is
double its velocity at 0°C.
Sol: Speed of velocity in air is, v ? vT 
3
2
3
Q2: Calculate the difference in the speeds of sound in air at -3°C, 60 cm
pressure of mercury and 30°C, 75 cm pressure of mercury. The speed of
sound in air at 0°C is 332 m/s.
Sol: v ? vT
? 
= 330.17 m/s
= 349.77 m/s
The difference in these two speeds is approximately 20 m/s.
Q3: In a liquid wit h density 900 kg/m , longitudinal waves with frequency
250 Hz are found to have wavelength 8.0 m. Calculate the bulk modulus of
the liquid.
Sol: 
? B = ? (f?)
= (900) (250 × 8) = 3.6 × 10 N/m
Q4: Calculate the speed of sound in oxygen at 273 K.
Sol: 
= 315 m/s
Introductory Exercise 16.3
Q1: A sound wave in air has a frequency of 300 Hz and a displacement
amplitude of 6.0 × 10 -3 mm. For this sound wave calculate the
(a) pressure amplitude
(b) intensity
(c) sound intensity level (in dB)
3
2
2 9 2
Page 4


Introductory Exercise 16.1
Q1: Calculate the bulk modulus of air from the following data for a sound
wave of wavelength 35 cm travelling in air. The pressure at a point varies
between (10 ± 14) Pa and the particles of the air vibrate in SHM of
amplitude 5.5 × 10 m.
Sol: 
Q2: Find the minimum and maximum wavelengths of sound in water that is
in the audible range for an average human ear. Speed of sound in water is
1450 m/s.
Sol: (a) For minimum wavelength n = 20 KHz
Q3: A typical loud sound wave with a frequency of 1 kHz has a pressure
amplitude of about 10 Pa (a) At t = 0, the pressure is a maximum at some
point x . What is the displacement at that point at t = 0?
5
-6
1
(b) What is the maximum value of the displacement at any time and place ?
Take the density of air to be 1.29 kg/m and speed of sound in air is 340
m/s.
Sol: (a) Displacement is zero when pressure is maximum.
Q4:  The pressure variation in a sound wave in air is given by
?P = 12 sin(8.18x - 2700t +p/4) N/m
Find the displacement amplitude. Density of air = 1.29 kg/m .
Sol: In the above problem, we have found that
Now substituting the value, we have
 
Introductory Exercise 16.2
Q1: Calculate the temperature at which the velocity of sound in air is
double its velocity at 0°C.
Sol: Speed of velocity in air is, v ? vT 
3
2
3
Q2: Calculate the difference in the speeds of sound in air at -3°C, 60 cm
pressure of mercury and 30°C, 75 cm pressure of mercury. The speed of
sound in air at 0°C is 332 m/s.
Sol: v ? vT
? 
= 330.17 m/s
= 349.77 m/s
The difference in these two speeds is approximately 20 m/s.
Q3: In a liquid wit h density 900 kg/m , longitudinal waves with frequency
250 Hz are found to have wavelength 8.0 m. Calculate the bulk modulus of
the liquid.
Sol: 
? B = ? (f?)
= (900) (250 × 8) = 3.6 × 10 N/m
Q4: Calculate the speed of sound in oxygen at 273 K.
Sol: 
= 315 m/s
Introductory Exercise 16.3
Q1: A sound wave in air has a frequency of 300 Hz and a displacement
amplitude of 6.0 × 10 -3 mm. For this sound wave calculate the
(a) pressure amplitude
(b) intensity
(c) sound intensity level (in dB)
3
2
2 9 2
Speed of sound = 344 m/s and density of air = 1.2 kg/m .
Sol: (a) 
  = 4.67 Pa
(b) 
(c) 
Q2: Most people interpret a 9.0 dB increase in sound intensity level as a
doubling in loudness. By what factor must the sound intensity be increased
to double the loudness?Sol: 
Given L - L =9 dB
Solving the equation we get,
Q3: A baby's mouth is 30 cm from her father's ear and 3.0 m from her
mother's ear. What is the, difference between the sound intensity levels
heard by the father and by the mother.
Sol: 
? 
3
2 1
Page 5


Introductory Exercise 16.1
Q1: Calculate the bulk modulus of air from the following data for a sound
wave of wavelength 35 cm travelling in air. The pressure at a point varies
between (10 ± 14) Pa and the particles of the air vibrate in SHM of
amplitude 5.5 × 10 m.
Sol: 
Q2: Find the minimum and maximum wavelengths of sound in water that is
in the audible range for an average human ear. Speed of sound in water is
1450 m/s.
Sol: (a) For minimum wavelength n = 20 KHz
Q3: A typical loud sound wave with a frequency of 1 kHz has a pressure
amplitude of about 10 Pa (a) At t = 0, the pressure is a maximum at some
point x . What is the displacement at that point at t = 0?
5
-6
1
(b) What is the maximum value of the displacement at any time and place ?
Take the density of air to be 1.29 kg/m and speed of sound in air is 340
m/s.
Sol: (a) Displacement is zero when pressure is maximum.
Q4:  The pressure variation in a sound wave in air is given by
?P = 12 sin(8.18x - 2700t +p/4) N/m
Find the displacement amplitude. Density of air = 1.29 kg/m .
Sol: In the above problem, we have found that
Now substituting the value, we have
 
Introductory Exercise 16.2
Q1: Calculate the temperature at which the velocity of sound in air is
double its velocity at 0°C.
Sol: Speed of velocity in air is, v ? vT 
3
2
3
Q2: Calculate the difference in the speeds of sound in air at -3°C, 60 cm
pressure of mercury and 30°C, 75 cm pressure of mercury. The speed of
sound in air at 0°C is 332 m/s.
Sol: v ? vT
? 
= 330.17 m/s
= 349.77 m/s
The difference in these two speeds is approximately 20 m/s.
Q3: In a liquid wit h density 900 kg/m , longitudinal waves with frequency
250 Hz are found to have wavelength 8.0 m. Calculate the bulk modulus of
the liquid.
Sol: 
? B = ? (f?)
= (900) (250 × 8) = 3.6 × 10 N/m
Q4: Calculate the speed of sound in oxygen at 273 K.
Sol: 
= 315 m/s
Introductory Exercise 16.3
Q1: A sound wave in air has a frequency of 300 Hz and a displacement
amplitude of 6.0 × 10 -3 mm. For this sound wave calculate the
(a) pressure amplitude
(b) intensity
(c) sound intensity level (in dB)
3
2
2 9 2
Speed of sound = 344 m/s and density of air = 1.2 kg/m .
Sol: (a) 
  = 4.67 Pa
(b) 
(c) 
Q2: Most people interpret a 9.0 dB increase in sound intensity level as a
doubling in loudness. By what factor must the sound intensity be increased
to double the loudness?Sol: 
Given L - L =9 dB
Solving the equation we get,
Q3: A baby's mouth is 30 cm from her father's ear and 3.0 m from her
mother's ear. What is the, difference between the sound intensity levels
heard by the father and by the mother.
Sol: 
? 
3
2 1
Now 
Substituting
 
We get, L - L - 20 dB
Q4: The faintest sound that can be heard has a pressure amplitude of about
2 × 10 N/m and the loudest that can be heard without pain has a
pressure amplitude of about 28 N/m . Determine in each case
(a) the intensity of the sound both in W/m and in dB and
(b) the amplitude of the oscillations if the frequency is 500 Hz. Assume an
air density of 1.29 kg/m and a velocity of sound is 345 m/s.
Sol: 
For finest sound,
= - 3.48 dB
Same formulae can be applied for loudest sound.
? 
For finest sound,
= 1.43 × 10 m
x1 2
-5 2
2
2 
3 
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