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Question

The amplitude of motion for the air in the path os a 60 dB, 800 Hz sound wave is 1.36×10x. Find x. Assume that ρair=1.29kg/m3 and ν=330m/s

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Solution

We have loudness of sound ,
L=log(I/I0) ,
or (I/I0)=10L ,
given L=60dB=6bel , and we know , I0=1012W/m2 ,
therefore ,
I/I0=106 ,
or I=1012×106=106W/m2 ,

now intensity , I=2π2f2A2ρv ,
given f=800Hz,v=330m/s,ρ=1.29kg/m3 ,
therefore ,
A2=I/(2π2f2ρv)=1062×3.142×8002×1.29×330=1.86×1016 ,
A=1.36×108m=13.6nm

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