Question

Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between (1.0 × 10⁵ ± 14) Pa and the particles of the air vibrate in simple harmonic motion of amplitude 5.5 × 10⁻⁶ m.

Answer 1

Given:

Wavelength of sound wave 

\[\lambda\]= 35 cm =\[35 \times  {10}^{- 2}   m\]

Pressure amplitude P₀ =\[1 . 0 \times  {10}^5  \pm 14  Pa\]

 

Displacement amplitude of the air particles S₀ = 5.5 × 10⁻⁶ m
Bulk modulus is given by:

\[B = \frac{P_0 \lambda}{2\pi S_0} = \frac{∆ p}{\left( ∆ V/V \right)}\]

On substituting the respective values in the above equation, we get:

\[B = \left( \frac{14 \times 35 \times {10}^{- 2} m}{2\pi\left( 5 . 5 \right) \times {10}^{- 6} m} \right)\] 

\[ \Rightarrow B = 1 . 4 \times  {10}^5   N/ m^2\]

Hence, the bulk modulus of air is 1.4\[\times\] 10⁵ N/m².