DC Pandey Solutions: Sound Waves - 1 - Notes | Study Physics Class 11 - NEET

Introductory Exercise 16.1

Q.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.
Sol:

Q.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.
Sol: (a) For minimum wavelength n = 20 KHz

Q.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.

Q.4:  The pressure variation 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

Q.1: 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 ∝ √T 

Q.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.

Q.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.
Sol: 
∴ B = ρ (fλ)²
= (900) (250 × 8)² = 3.6 × 10⁹ N/m²

Q.4: Calculate the speed of sound in oxygen at 273 K.
Sol: 

= 315 m/s

Introductory Exercise 16.3

Q.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
(b) intensity
(c) sound intensity level (in dB)
Speed of sound = 344 m/s and density of air = 1.2 kg/m³.
Sol: (a)

  = 4.67 Pa

(b)

(c)

Q.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,


Q.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.
Sol: 
∴
Now
Substituting
 
We get, L_x1 - L₂ - 20 dB

Q.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.
Sol: 

For finest sound,


= - 3.48 dB
Same formulae can be applied for loudest sound.


∴
For finest sound,

= 1.43 × 10^-11 m