Audio Decay Time (T60)

In audio, a decay by $1/e$ is not enough to become inaudible, unless the starting amplitude was extremely small. In architectural acoustics (which includes the design of concert halls), a more commonly used measure of decay is ``$t_{60}$'' (or T60), which is defined as the time to decay by $60$ dB.^4.6That is, $t_{60}$ is obtained by solving the equation

$$\frac{a(t_{60})}{a(0)} = 10^{-60/20} = 0.001.$$

Using the definition of the exponential $a(t) = A e^{-t/\tau}$, we find

$$\zbox {t_{60} = \ln(1000) \tau \approx 6.91 \tau}$$

Thus, $t_{60}$ is about seven time constants. See where $t_{60}$ is marked on Fig. 4.5 compared with $\tau$.