Relating to the $T_{60}$

For audio/music, it is more useful to define the time constant as the time it takes to decay -60dB, or 0.001 times the initial value.

The attenuation factor at time $t = T_{60}(f)$ is given by

$$\alpha_f(T_{60}(f)) = 0.001.$$

Conversion from $\tau$ to $T_{60}$ is done by

$$0.001 = e^{-T_{60}/\tau}$$

$$\ln(0.001) = -\frac{T_{60}}{\tau}$$

$$T_{60} = -\ln(0.001)\tau$$

$$\approx 6.91\tau$$