Chirp Equation: Solving Waveform Frequency Changes

[Panda]

Can anyone give me a general equation for a sinusoidal chirp.

I want to calculate a waveform where the frequency drops a given fraction over a given number of cycles.

 

[Crosson]

A chirp is a sinusoidal signal whose frequency changes with time.

For example, a linear chirp has the form $$A Sin(a t^2)$$ because its frequency $$at$$ is a linear function of time.

A chirp for which the frequency decreased by a fixed fraction per time would involve exponential decay i.e. the frequency would have a half life. These chirps sound like space-blaster sound effects.