# Acoustic intensity

The power per unit area that is delivered to a medium, where the area is perpendicular to the direction of wave travel. To have meaning, the location where the intensity is measured must be specified with respect to the acoustic source. The medium is often a fluid. (Kinsler, p. 110)

If the specified location is at the surface of the acoustic source, then the average acoustic intensity at the interface between the source and the medium is —

\begin{align} \label{eq:11301a} \textsf{Acoustic intensity (average)} = \frac{\textsf{Power delivered to the medium}}{\textsf{Area from which the power is delivered}} \end{align}

For a given resonator material and load, a higher source acoustic intensity will result in greater wear of the source resonator, assuming that the wear mechanism is the same.

The following examples illustrate increasing levels of acoustic intensity.

## Example 1

A 20 kHz ultrasonic cleaner has an active area of 100 mm x 100 mm. With a water load, the delivered power is 75 watts. The average acoustic intensity is —

\begin{align} \label{eq:11302a} \textsf{Acoustic intensity} &= \frac{\textsf{75 watts}}{\textsf{10000 mm}^2} \\[0.7em]%eqn_interline_spacing &= \textsf{0.0075 watts/mm}^2 \nonumber \end{align}

## Example 2

A 20 kHz cylindrical horn (10 mm face diameter) has an amplitude of 100 microns. When the face is immersed in water, 200 watts of power are delivered. The acoustic average intensity is —

\begin{align} \label{eq:11303a} \textsf{Acoustic intensity} &= \frac{\textsf{200 watts}}{\textsf{79 mm}^2} \\[0.7em]%eqn_interline_spacing &= \textsf{2.5 watts/mm}^2 \nonumber \end{align}

## Example 3

A 20 kHz metal welding horn (8 mm x 8 mm contact area) has an amplitude of 100 microns. During welding, 900 watts of power are delivered. The acoustic intensity is —

\begin{align} \label{eq:11304a} \textsf{Acoustic intensity} &= \frac{\textsf{900 watts}}{\textsf{64 mm}^2} \\[0.7em]%eqn_interline_spacing &= \textsf{14 watts/mm}^2 \nonumber \end{align}