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.
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]A^{2}[itex]\rho[/itex] c