Question

If it were possible to generate a sinusoidal 300 Hz sound wave in air that has a displacement amplitude of 0.200 mm. The sound level of the wave would be $1.344\times {10}^{x}dB$ . Find x. $(Assume\nu =330m/s$ and ${\rho }_{a}ir=1.29kg/m^3)$

Answer 1

Given - $f=300Hz,A=0.200mm=2\times {10}^{-4}m,v=330m/s,\rho =1.29kg/m^3$ ,

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

$I=2\times {3.14}^2\times {300}^2\times (2\times {10}^{-4}{)}^2\times 1.29\times 330=30.22W/m^2$ ,

therefore sound level ,

$L=10log\left(I/I_0\right)$ , (where , $I_0={10}^{-12}W/m^2$) ,

$L=10log\left(30.22/{10}^{-12}\right)=10(log30.22+log{10}^{12})$ ,

or $L=10(1.48+12)=134.8dB$