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Question

A bomb blast gives a sound of intensity 0.8 W/m2 and frequency 1.5 kHz. If the density of air is 1.25 kg/m3 and speed of sound in air is 330 m/s, then the amplitude of the sound wave is approximately

A
4.4 μm
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B
5.5 μm
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C
6.6 μm
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D
7.7 μm
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Solution

The correct option is C 6.6 μm
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=0.82×3.142×(1.5×103)2×1.25×330
Ao=6.6×106 m=6.6 μm

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