My first damped sine wave

How does the time constant of a damped sine wave influence its shape and sound? Let us try...

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$\\sin(2 \\pi 200 t) e^{-t/\\tau}$

Damped sine wave

Open for comments

Damping signal $f$ is defined as:

$$ f_d(t) = f(t)\,e^{-t/tau} $$

Its time constant $tau$ is such that:

$$ f_d(t) \approx 0 \text{ for } t > 5\tau $$

and that:

$$ f_d'(t=0) = -1 / \tau $$

This means that the tangent of the envelope of $f(t)$ at $t=0$ is as shown in orange on the plot.