# What is the Acoustic intensity and how to calculate it

Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that area. The SI unit of intensity, which includes sound intensity, is the watt per square meter (w/m2). 1

The power per unit area delivered to a medium, where the area is perpendicular to the direction of wave travel. The location where the intensity is measured must be specified concerning the acoustic source to have meaning.

### How to calculate Acoustic intensity

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 Sound 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 Sound intensity.

A 28 kHz ultrasonic cleaner has an active 50 mm x 50 mm. With a water load, the delivered power is 55 watts. The average Sound 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}

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}

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}

#### References

1. reference material wikipedia