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Power and Amplitude of sound wave 
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#1
Nov605, 12:30 AM

P: 8

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. 


#2
Nov705, 08:20 AM

Admin
P: 21,827

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 


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