Question

Show that the sound wave intensity I can be written in terms

of the frequency f and displacement amplitude dm in the form, I = 2pi

vf ^2s^2 m.

Answer 1

Energy of oscillation over time:

$$\frac ET=\frac1{2T} mA^2(2\pi f)^2.$$

Intensity is energy over area:

$$I=2\pi^2\rho f^2vs^2.$$