Introductory Exercise 16.1
Ques 1: 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 (105 ± 14) Pa and the particles of the air vibrate in SHM of amplitude 5.5 × 10-6 m.
= 1.4 × 105N/m2
Ques 2: 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.
= 0.0725 m = 7.25 cm
Ques 3: 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 x1. What is the displacement at that point at t = 0?
(b) What is the maximum value of the displacement at any time and place ? Take the density of air to be 1.29 kg/m3 and speed of sound in air is 340 m/s.
Sol: (a) Displacement is zero when pressure is maximum.
= 3.63 × 10-6 m
Ques 4: The pressure variat ion in a sound wave in air is given by
ΔP = 12 sin(8.18x - 2700t +π/4) N/m2
Find the displacement amplitude. Density of air = 1.29 kg/m3.
Sol: In the above problem, we have found that
Now substituting the value, we have
Introductory Exercise 16.2
Ques 1: Calculate the temperature at which the velocity of sound in air is double its velocity at 0°C.
Sol: v ∝ √T
= 1092 K = 819°C
Ques 2: 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 ∝ √T
= 330.17 m/s
= 349.77 m/s
The difference in these two speeds is approximately 20 m/s.
Ques 3: In a liquid wit h density 900 kg/m3, longitudinal waves with frequency 250 Hz are found to have wavelength 8.0 m. Calculate the bulk modulus of the liquid.
∴ B = ρ (fλ)2
= (900) (250 × 8)2 = 3.6 × 109 N/m2
Ques 4: Calculate the speed of sound in oxygen at 273 K.
= 315 m/s
Introductory Exercise 16.3
Ques 1: 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
(c) sound intensity level (in dB)
Speed of sound = 344 m/s and density of air = 1.2 kg/m3.
= 4.67 Pa
(as B= ρv2)
= 0.0264 W/m2 = 2.64 × 10-2 W/m2
= 104 dB
Ques 2: 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 L2 - L1 =9 dB
Solving the equation we get,
Ques 3: 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.
We get, Lx1 - L2 - 20 dB
Ques 4: The faintest sound that can be heard has a pressure amplitude of about 2 × 10-5 N/m2 and the loudest that can be heard without pain has a pressure amplitude of about 28 N/m2. Determine in each case
(a) the intensity of the sound both in W/m2 and in dB and
(b) the amplitude of the oscillations if the frequency is 500 Hz. Assume an air density of 1.29 kg/m3 and a velocity of sound is 345 m/s.
For finest sound,
= - 3.48 dB
Same formulae can be applied for loudest sound.
For finest sound,
= 1.43 × 10-11 m