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Question

Find the displacement amplitude of particles of air of density 1.5 kg/m3 if the intensity and frequency of sound are 8×106 W/m2 and 5000 Hz respectively.
[speed of sound in air =330 m/s]

A
5.7 nm
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B
4.7 nm
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C
3.7 nm
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D
2.7 nm
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Solution

The correct option is A 5.7 nm
We know that the intensity of sound is given by,
I=12ρω2A2ov,
where, ρ is the density of medium, ω is the angular frequency of sound, Ao is the displacement amplitude of particles of medium and v is the speed of sound.
I=2π2f2ρA2ov
[ ω=2πf ]
Ao=I2π2f2ρv
Ao=8×1062×3.142×50002×1.5×330
Ao=5.7×109 m=5.7 nm

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