Question

The amplitude of motion for the air in the path os a 60 dB, 800 Hz sound wave is $1.36\times {10}^x$. Find x. Assume that ${\rho }_{air}=1.29kg/m^3$ and $\nu =330m/s$

Answer 1

We have loudness of sound ,

$L=log\left(I/I_0\right)$ ,

or $\left(I/I_0\right)={10}^L$ ,

given $L=60dB=6bel$ , and we know , $I_0={10}^{-12}W/m^2$ ,

therefore ,

$I/I_0={10}^6$ ,

or $I={10}^{-12}\times {10}^6={10}^{-6}W/m^2$ ,

now intensity , $I=2{\pi }^2{f}^2{A}^2\rho v$ ,

given $f=800Hz,v=330m/s,\rho =1.29kg/m^3$ ,

therefore ,

$A^2=I/\left(2{\pi }^2{f}^2\rho v\right)=\frac{{10}^{-6}}{2\times {3.14}^2\times {800}^2\times 1.29\times 330}=1.86\times {10}^{-16}$ ,

$A=1.36\times {10}^{-8}m=13.6nm$