Power and Amplitude of sound wave

[Trooko]

For my homework,
To find Amplitude of the wave,
for a longitudinal wave traveling 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:

$$A\,=\,\frac{\Delta{p_o}}{\omega\,\rho\,c}$$, where

$\Delta{p_o}$ is the pressure amplitude,

$\omega$ is the angular frequency given by $2\,\pi\,f$,

$\rho$ is the material density, and

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

$$c = \sqrt{\frac{E}{\rho}}$$

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 $\omega^2$A²$\rho$ c

 

[piercas]

Hello! I would like to provide some clarification on the concepts of power and amplitude in relation to sound waves.

Firstly, power refers to the rate at which energy is transferred or the amount of energy per unit time. In the case of sound waves, power is directly proportional to the amplitude of the wave, which is the maximum displacement of the particles in the medium from their equilibrium position. This means that the greater the amplitude of the sound wave, the more energy it carries.

Now, let's consider the equation you mentioned, P=(omega*amplitude)^2. This equation is not entirely accurate because it only considers the angular frequency (omega) and the amplitude of the wave. In reality, the power of a sound wave is also affected by other factors such as the medium it travels through and the distance it travels.

In order to accurately calculate the power of a sound wave traveling through a copper rod, we need to consider the following equation: P = A^2 * (rho * c * f^2), where A is the amplitude, rho is the density of the medium (in this case, copper), c is the speed of sound in the medium, and f is the frequency of the wave. This equation takes into account the properties of the medium and the frequency of the wave to accurately determine the power of the sound wave.

I hope this helps with your homework and provides a better understanding of the relationship between power and amplitude in sound waves. Keep up the good work in your studies!