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Question

Find the amplitude of motion of the air in the path of a 40 dB,1000 Hz sound wave.
[Assume that the density of air is 1.3 kg/m3 and speed of sound in 340 m/s].

A
1 cm
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B
1 μm
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C
1 nm
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D
1 mm
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Solution

The correct option is C 1 nm
Given that,
ρ=1.3 kg/m3 , v=340 m/s , f=1000 Hz & β=40 dB.

From the relation between loudness and the intensity of sound wave,
β=10log10(II0)
From the data given,
40=10log10(I1012)
I=1012×104=108 W/m2

Using Intensity formula,
I=12ρω2vA2
A=2Iρω2v=2Iρ(2πf)2v

Substituting the data, we get

A=2×1081.3×(2π×1000)2×340109 m or 1 nm

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