Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

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  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-04-06 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA