# Displacement and pressure in sound wave

1. Dec 17, 2003

### 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)

2. Dec 17, 2003

### 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
$$\Delta p_m=\omega v \rho s_m$$

Last edited: Dec 17, 2003