Find the displacement amplitude of particles of air of density 1.5kg/m3 if the intensity and frequency of sound are 8×10−6W/m2 and 5000Hz respectively. [speed of sound in air =330m/s]
A
5.7nm
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B
4.7nm
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C
3.7nm
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D
2.7nm
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Solution
The correct option is A5.7nm 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=√8×10−62×3.142×50002×1.5×330 ⇒Ao=5.7×10−9m=5.7nm