Free Books
   Free Books    Mathematics of the DFT  

Audio Decay Time (T60)

In audio, a decay by $ 1/e$ (one time-constant) is not enough to become inaudible, unless the starting amplitude was extremely small. In architectural acoustics (which includes the design of concert halls [4]), a more commonly used measure of decay is ``$ t_{60}$'' (or T60), which is defined as the time to decay by $ 60$ dB.4.7That is, $ t_{60}$ is obtained by solving the equation

$\displaystyle \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

$\displaystyle \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.4.7 compared with $ \tau$.

Next Section:
Circular Motion
Previous Section:
Why Exponentials are Important