Plane harmonic waves of frequency 500 Hz are produced in air with displacement amplitude of 10 $\mathrm{\mu }$m. Given that density of air is 1.29 kg/m³ and speed of sound in air is 340 m/s. Then

Pressure amplitude

      ${\mathrm{P}}_0=\frac{2\mathrm{\pi aE}}{\mathrm{\lambda }}$

where E is the coefficient of elasticity. We have,

        $\mathrm{E}={\mathrm{v}}^2\mathrm{\rho }\left\{\because \mathrm{v}=\sqrt{\frac{\mathrm{E}}{\mathrm{\rho }}}\right\}$

 $\therefore {\mathrm{P}}_0=\frac{2{\mathrm{\pi av}}^2\mathrm{\rho }}{\mathrm{\lambda }}=\frac{2{\mathrm{\pi av}}^2\mathrm{\rho }}{\left(\frac{\mathrm{v}}{\mathrm{f}}\right)}$

$\Rightarrow {\mathrm{P}}_0=2\mathrm{\pi avf\rho }=13.8 \mathrm{N}/{\mathrm{m}}^2$

Energy density is $2{\mathrm{\pi }}^2{\mathrm{a}}^2{\mathrm{f}}^2\mathrm{\rho }=6.4\times {10}^{-4}\mathrm{J}/{\mathrm{m}}^3$

Energy flux is $2{\mathrm{\pi }}^2{\mathrm{a}}^2{\mathrm{f}}^2\mathrm{\rho v}=0.22\mathrm{J}/\left({\mathrm{m}}^2/\mathrm{s}\right)$