Question

The intensity of sound wave whose frequency is $250Hz$ is $\frac{{\pi }^2\times {10}^{-9}}{x}W/m^2$. The displacement amplitude of particles of the medium at this position is $1\times {10}^{-8}m$. The density of the medium is $1kg/m^3$, bulk modulus of elasticity of the medium is $400N/m^2$. Find $x$

Answer 1

Given: $\nu =250Hz\rho =1kg/m^3{s}_o=1\times {10}^{-8}m$

Bulk modulus of elasticity $B=400N/m^2$

Velocity of the sound in the medium $v=\sqrt{\frac{B}{\rho }}=\sqrt{\frac{400}{1}}m/s$

$⟹v=20m/s$

Intensity of sound wave $I=2{\pi }^2{\nu }^2{s}_o^2\rho v$

$I=2{\pi }^2\times (250{)}^2\times ({10}^{-8}{)}^2\times 1\times 20$

$⟹I=0.25{\pi }^2\times {10}^{-9}W/m^2$

Thus $x=\frac{1}{0.25}=4$