Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# 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 - Physics

Sum

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.

#### Solution

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.

Concept: Wave Motion
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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 16 Sound Waves
Q 16 | Page 353