Question

a) Calculate the intensity of a wave traveling in the air with an amplitude of 2 mm, a frequency of 400 Hz and at a speed of 150 m/sec.

Density of air at sea level is 1.225 Kg/m³.

Answer 1

The intensity of the longitudinal (or sound) wave can be found as follows:

$$I=\dfrac{1}{2}\rho_{air}\omega^2A^2v=\dfrac{1}{2}\rho_{air}(2\pi f)^2A^2v,$$ $$I=2\pi^2\rho_{air}f^2A^2v,$$ $$I=2\pi^2\times1.225\ \dfrac{kg}{m^3}\times(400\ Hz)^2\times(2\times10^{-3}\ m)^2\times150\ \dfrac{m}{s},$$ $$I=2321\ \dfrac{W}{m^2}.$$