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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 5×10−3 N/m2 and the amplitude of vibration of the particles of the medium is 5×10−10 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/m2Given, Wavelength, λ=50 cm Displacement amplitude, A0=5×10−10 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=Pmax−Pmin2 Po=5×10−32 Po=2.5×10−3 N/m2 Also, k=2πλ=2π0.5=4π Hence, B=P0kA0 B=2.5×10−34×3.14×5×10−10 B=3.98×105 N/m2 B≈4×105 N/m2

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