# Gain

In general (for any system):

\begin{align} \label{eq:10401} \textsf{Gain} = \frac{\textsf{Output}}{\textsf{Input}} \end{align}

For ultrasonic resonators the gain indicates an amplitude ratio:

\begin{align} \label{eq:10402} \textsf{Gain} = \frac{\textsf{Output amplitude}}{\textsf{Input amplitude}} \end{align}

or, sometimes, a velocity ratio:

\begin{align} \label{eq:10403} \textsf{Gain} = \frac{\textsf{Output velocity}}{\textsf{Input velocity}} \end{align}

For a given resonator, equations \eqref{eq:10402} and \eqref{eq:10403} give the same value.

Unless otherwise specified —

1. All amplitudes are axial.
2. The output amplitude is measured at the center of the face.
3. The input amplitude is measured at the center of the stud surface .

If a resonator is said to have gain but no specific value is mentioned, the gain is assumed to be greater than 1.0 (i.e., forward gain) (If the gain is less than 1.0 then the resonator is said to have reverse gain.)

Synonyms — amplification factor, transmutation ratio