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lecture5

# lecture5 - Lecture 5 Notes 07 05 Energy and intensity of...

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Lecture 5 Notes: 07 / 05 Energy and intensity of sound waves Sound waves carry energy, just like waves on a string do. This energy comes in several types: potential energy due to the compression of the material, kinetic energy due to the movement of the material's particles, and also thermal energy, since when the material is compressed it heats up a bit. Just like for waves on a string, the energy carried by sound waves increases with amplitude and frequency; however, we won't derive the precise relationship here. Let us say that a material with a sound wave traveling through it has an acoustic energy density ρ E . On a string, this had units of energy per length, or J / m. However, a sound wave travels through a three-dimensional, rather than a one-dimensional, medium, so the units are now energy per volume, or J / m 3 . Consider an plane of area A , perpendicular to the direction of propagation of the wave: Assume that A is sufficiently small that the amplitude and direction of travel of the wave is uniform throughout it. Then, the rate at which energy is transported across the surface A (called the energy flux across A ) is: The energy flux has units of (J / m 3 ) x (m 2 ) x (m / s) = J / s = W, as expected (since the flux is a rate at which energy is transported). The intensity is defined as energy flux per unit area: The intensity has units of W / m 2 , and measures how loud (intense) the sound is.

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Sound comes in a huge range of intensities. For example, the human ear can detect sounds with an intensity of about 10 -12 W/m 2 (this is called the threshold of hearing ). There are, of course, inaudible sounds that have much lower intensities than this. The ear can handle, at least for a short while, sounds with an intensity up to about 1 W/m 2 . Sounds with intensities much above 1 W/m 2 are very uncomfortable to be around without earplugs, and can quickly cause hearing damage. Standing close to a jet engine or a firing artillery piece can expose one to sound intensities in excess of thousands of W / m 2 . Such sound waves can instantly rupture the eardrum unless appropriate ear protection is used (opening the mouth also helps, as the sound wave can then reach both the inside and the outside of the eardrum at the same time, possibly preventing it from being ruptured.) Since we want to be able to describe sounds which differ in intensity by more than 16 orders of magnitude, it is useful to introduce a logarithmic scale. The intensity level is given in decibels, and defined as follows: Thus, a sound on the threshold of hearing has an intensity level of about 0 decibels.
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