The loudest painless sound produces a pressure amplitude of `28 Nm^2`. Calculate the intensity of this sound wave at S.T.P. Density of air at ST.P.=` 1.3 kg m^(-3)` speed of sound at S.T.P.= 332 m/s.

Explanation

`y=a sin (omegat -kx)` is the equation of progressive wave of 1/2 `rhoa^2omega^2v` is its intensity
`P=(Edy)/(dx), v=sqrt(E/rho)`
`=v^2 rho (-ak) (cos omegat-kx)=v^2 rho ak sin (omegat-kx-pi//2)`
`therefore P_(max)=v^2 rho ak`
`therefore l=1/2rho(P_"max"^2)/(v^4 rho^2 k^2) v^2k^2 v " " {omega/k=v}`
`=1/2 rho_"max"^2/(rhov) =1/2 xx28^2/(1.3xx332)=0.91 W-m^2`