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

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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
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