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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 B 4×105 N/m2
Given that,
Wavelength, λ=50 cm
Displacement amplitude, S0=5×1010 m
Pressure amplitude P0=BkS0
where B is bulk modulus of the medium and k is wave number.
P0=PmaxPmin2
=5×1032
=2.5×103 N/m2.
k=2πλ=2π0.5=4π

Hence, B=P0kS0
=2.5×1034×3.14×5×1010
=3.98×105 N/m2
4×105 N/m2

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