Question

A sound wave of wavelength 40 cm travels in air. If the difference between maximum and minimum pressures at a given point is 1.0×10−3 N/m2, then find the amplitude of vibrations of the particles of the medium. [Bulk modulus of air is 1.4×105 N/m2]

A
3.3×1010 m
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B
2.3×1010 m
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C
4.3×1010 m
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D
5.3×1010 m
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Solution

The correct option is B 2.3×10−10 m Let P be the atmospheric pressure. Difference between maximum and minimum pressures at a given point, [(P+Po)−(P−Po)]=1.0×10−3 N/m2 ⇒2Po=1.0×10−3 N/m2 ⇒Po=0.5×10−3 N/m2 We know the relation between maximum value of pressure in the medium and displacement of the particles in the medium is given by, Po=BAok ⇒Ao=PoBk=λPo2πB ⇒Ao=40×10−2×0.5×10−32×3.14×1.4×105 ⇒Ao=2.3×10−10 m

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