Power and Amplitude of sound wave

Trooko

For my homework,
To find Amplitude of the wave,
for a longitudinal wave travelling down a copper rod.
Given: frequency, radius of copper rod, average power, Young's constant, density, wavelength.
what equation should I consider?
I'm thinking something like P=(omega*amplitud)^2 because I know power is proportional to amplitude and frequency of the wave....but I know that's wrong.

Astronuc

The displacement amplitude A is given by:

[tex]A\,=\,\frac{\Delta{p_o}}{\omega\,\rho\,c}[/tex], where

[itex]\Delta{p_o}[/itex] is the pressure amplitude,

[itex]\omega[/itex] is the angular frequency given by [itex] 2\,\pi\,f[/itex],

[itex]\rho[/itex] is the material density, and

c = speed of sound in the material, which is given by -

[tex] c = \sqrt{\frac{E}{\rho}}[/tex]

where E is Young's (Elastic) modulus.


The intensity of the sound wave is I = P/a, where P is the power of the wave per unit transverse area, a, and

P = 1/2 [itex]\omega^2[/itex]A²[itex]\rho[/itex] c