displacement and pressure in sound wave

[denian]

there is one formula given as follow

(max pressure ) = (speed of wave)X(density of medium)X(angular frequency of the wave ) X (maximum displacement)

in the book, there is no working shown how to arrive to this formula. anyone can show me the steps? thank you.


(sorry, i dont know how to insert the symbols)

[himanshu121]

consider


s=s_m\sin(kx-\omega t)

\Delta p=-B\frac{ds}{dx}

\Delta p(x,t) = Bks_m\sin(kx-\omega t)


B=\rho v^2


k=\frac{\omega}{v}

hence u get
\Delta p_m=\omega v \rho s_m