JEE Main & Advanced Physics Wave Mechanics Pressure Waves

A longitudinal sound wave can be expressed either in terms of the longitudinal displacement of the particles of the medium or in terms of excess pressure produced due to compression or rarefaction. (at compression, the pressure is more than the normal pressure of the medium and at rarefaction the pressure is lesser than the normal). The first type is called the displacement wave and the second type the pressure wave.

If the displacement wave is represented by \[y=a\sin (\omega \,t-kx)\] then the corresponding pressure wave will be represented by \[\Delta P=-\,B\frac{dy}{dx}\] (B = Bulk modulus of elasticity of medium)

\[\Rightarrow \]\[\Delta P=\Delta {{P}_{0}}\cos (\omega \,t-kx)\]

where \[\Delta {{P}_{0}}=\]pressure amplitude \[=akB\]

Pressure wave is \[\left( \frac{\pi }{2} \right)\] out of phase with displacement wave. i.e. pressure is maximum when displacement is minimum and vice-versa.