Acoustic Intensity

Acoustic intensity may be defined by

$$\zbox {\underline{I} \isdefs p \underline{v}} \quad \left(\frac{\mbox{\small Energy Flux}}{\mbox{\small Area}\cdot\mbox{\small Time}} \eqsp \frac{\mbox{\small Power Flux}}{\mbox{\small Area}}\right)$$

where

$$\begin{eqnarray*} p &=& \mbox{acoustic pressure} \quad \left(\frac{\mbox{\small Force}}{\mbox{\small Area}}\right)\\ \underline{v}&=& \mbox{acoustic particle velocity} \quad \left(\frac{\mbox{\small Length}}{\mbox{\small Time}}\right). \end{eqnarray*}$$

For a plane traveling wave, we have

$$\zbox {p = R v}$$

where

$$\zbox {R \isdefs \rho c}$$

is called the wave impedance of air, and

$$\begin{eqnarray*} c &=& \mbox{sound speed},\\ \rho &=& \mbox{mass density of air} \quad \left(\frac{\mbox{\small Mass}}{\mbox{\small Volume}}\right),\\ v &\isdef & \left\vert\underline{v}\right\vert. \end{eqnarray*}$$

Therefore, in a plane wave,

$$\zbox {I = p v = Rv^2 = \frac{p^2}{R}.}$$