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Question

A sound wave of wavelength 50 cm travels in a gas medium. If the difference between the maximum and minimum pressures at a given point is 5×103 N/m2 and the amplitude of vibration of the particles of the medium is 5×1010 m, find bulk modulus of the medium.

A
105 N/m2
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B
2×105 N/m2
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C
3×105 N/m2
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D
4×105 N/m2
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Solution

The correct option is D 4×105 N/m2
Given,

Wavelength, λ=50 cm

Displacement amplitude, A0=5×1010 m

We know that the relation between maximum pressure in the medium and maximum displacement of the particles in the medium is given by,

Po=BAok

where, Po is the maximum pressure, B is the bulk modulus, Ao is the maximum displacement and k is the wave number.

Po=PmaxPmin2

Po=5×1032

Po=2.5×103 N/m2

Also, k=2πλ=2π0.5=4π

Hence, B=P0kA0

B=2.5×1034×3.14×5×1010

B=3.98×105 N/m2

B4×105 N/m2

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