Sound intensity

Sound intensity is the time-averaged acoustic energy flux, a vector measured in $\mathrm{W}{\mathrm{m}}^{-2}$. In linear acoustics, $\mathbf{I}=⟨p^{\prime }{\mathbf{u}}^{\prime }⟩$, where $p^{\prime }$ is acoustic pressure and ${\mathbf{u}}^{\prime }$ particle velocity. Its direction identifies net energy transport, and integrating its normal component over a surface gives the acoustic power crossing that surface.

A progressive plane acoustic wave satisfies $I=p_{\mathrm{rms}}^2/(\rho c)$, with mean mass density $\rho$ and sound speed $c$. This formula uses the relation between pressure and velocity for that particular travelling field. Two opposite equal waves instead form a standing wave with zero net sound intensity, despite nonzero root mean square pressure. A microphone alone measures pressure; inferring transported power from it therefore requires assumptions about the field, especially near reflecting boundaries.