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Doppler Effect

The Doppler effect causes the pitch of a sound source to appear to rise or fall due to motion of the source and/or listener relative to each other. You have probably heard the pitch of a horn drop lower as it passes by (e.g., from a moving train). As a pitched sound-source moves toward you, the pitch you hear is raised; as it moves away from you, the pitch is lowered. The Doppler effect has been used to enhance the realism of simulated moving sound sources for compositional purposes [80], and it is an important component of the ``Leslie effect'' (described in §5.9).

As derived in elementary physics texts, the Doppler shift is given by

$\displaystyle \omega_l = \omega_s \frac{1+\frac{v_{ls}}{c}}{1-\frac{v_{sl}}{c}} \protect$ (6.2)

where $ \omega_s $ is the radian frequency emitted by the source at rest, $ \omega_l $ is the frequency received by the listener, $ v_{ls}$ denotes the speed of the listener relative to the propagation medium in the direction of the source, $ v_{sl}$ denotes the speed of the source relative to the propagation medium in the direction of the listener, and $ c$ denotes sound speed. Note that all quantities in this formula are scalars.



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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-06-11 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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