Can anyone clarify what does mean the angular frequency of a system in case of the vibrating membrane.
Angular frequency is measured in radians per second, what does this have with the vertical displacement in case of the wave equation.
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Sign up to join this communityCan anyone clarify what does mean the angular frequency of a system in case of the vibrating membrane.
Angular frequency is measured in radians per second, what does this have with the vertical displacement in case of the wave equation.
It is related to frequency by means of
$$ f = \frac{\omega}{2\pi} $$
and it is used in trig. functions like $\sin( \omega \cdot t)$ instead of $\sin( 2\pi f \cdot t)$ because it is simpler.
Angular frequency applies to any sinusoidally varying with time frequency when the arguments of the trigonometric functions are in radians. For an "angle" or geometric interpretation: the trig function variation is the real part of the phasor quantity $\exp(i\,\omega\,t)$, which follows the unit circle at constant speed $\omega$ radians per second, and so this is the rate of increase of the angle this number's position vector makes with the $x$-axis, so we can be still talking about a true angle here.