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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 and 14) Pa and the particles of the air vibrate in simple harmonic motion of amplitude 5.5× 106 m.


A

3.2 x 102 N/m2

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B

5.5 x 106 N/m2

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C

1.4 x 105 N/m2

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D

None of these

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Solution

The correct option is C

1.4 x 105 N/m2


Given

Wavelength λ=35cm

=35×102m

ΔP=(1.0×105 14)Pa

soP0 = 14 Pa

S0 = 5.5× 106 m

To find Bulk modulus

Relation between pressure and displacement amplitude

P0=BKS0 K=2πλ

14=B2π35×102×5.5×106

B = 1.4× 105 Nm2


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