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Is the intensity of a sound wave same at all the points through which the wave travels? The formula for intensity is $ I = \frac{{p_0}^2 }{2 \rho v}$. But this does not make sense to me. Shouldn't the intensity of sound depend upon the displacement of particles at that point, and also the pressure at that point at that instant?

EDIT: $p_0$ is the pressure amplitude, $\rho $ is the density of the medium, $ v$ is the velocity of the wave.

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Intensity is defined to be the average energy passing through a unit area per second. The key here is average. By defining it this way, we avoid intensity that varies with every period. The average intensity doesn't change unless the source changes it. In calculating the intensity the r.m.s. average pressure is calculated, and this is proportional to $p_o$.

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