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Figure 1. Longitudinal wave (http://www.acs.psu.edu/drussell/demos/waves/wavemotion.html)
Math
Sound wave has its own intensity which is defined by common word sound level. Sound intensity (I) is gotten by following pattern:
Sound level is gotten by following pattern:
Sound pressure in any media is not constant. It changes continuously. For that we have acoustic pressure (P) which is the difference between the instantaneous and the average pressure. Particle displacement (ξ) is particles distance of a movement from an equilibrium position (spot where wave hits first). With these two characteristics we can calculate intensity of a sound (I) which is the transferred power per unit area.
Acoustic pressure:
I=Pξ
Sound intensity level (SIL) is logarithm of ratio of sound intensity to sound intensity standard reference value (I0).
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Sources
Handbook of Modern Sensors by Jacob Fraden,2010, Springer
http://en.wikipedia.org/wiki/Sound_intensity
http://en.wikipedia.org/wiki/Sound_pressure
http://www.acs.psu.edu/drussell/demos/waves/wavemotion.html
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