# Amplitude Decay Modeling

Basic premise: a pure tone sine wave can be modeled with a pendulum and the rate of amplitude decay can be manipulated with a friction coefficient.

So... does anyone know how this is actually done? In other words if you picked a pure tone (let's say middle C @ 261.6 Hz) initiated at a certain dB (let's say 50dB), how would you factor in rate of decay and how would you replicate this with a literal physical pendulum?

I know this is a complex question and I'm not even sure anyone is doing this but there's got to be equations and computer modeling that does. Obviously I'm just learning about this so the simplest explanation possible would be wonderful. 1st post here btw, so I hope it's in the right area :) Thanks!

## Answers and Replies

Here's something...

Frequency of a pendulum = $$\frac{1}{2\pi}\sqrt{\frac{g}{L}}$$

So, the length of your pendulum will be about 3.6 microns.

The decibel level depends on your distance. The logic would be

Intensity level => intensity => power => energy => amplitude

So this could tell you how far the pendulum moves (if large--which it probably is--it may invalidate the previous formula), but not the rate of decay.