Find the amplitude of the vibration of the particles of air through which a sound wave of intensity `2.0xx10^-6Wm^-2` and frequency 1.0kHz is passing. Density of air =1.2 kgm^-3 and speed of sound in air `=330 ms^-1`.

Explanation

The relation between the intensity of sound and the displacement amplitude is
`I=2pi^2s_0^2v^2rho_0v`
or, s_0^2=I/(2pi^2v^2rho_0v)`
`=(2.0xx10^-6Wm^-2)/(2pi^2xx(1.0xx10^6s^2)xx(1.2kgm^-3)xx(330ms^-2))`
`=2.53xx10^-16m^2`
`or s_0=1.6xx10^-8m`.