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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$.


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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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