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 [83], and it is an important component of the ``Leslie effect'' (described in §3.4.7).

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

where is the radian frequency emitted by the source at rest, is the frequency received by the listener, denotes the speed of the listener relative to the propagation medium in the direction of the source, denotes the speed of the source relative to the propagation medium in the direction of the listener, and denotes sound speed. Note that all quantities in this formula are scalars.

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Subsections

• Vector Formulation

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written by 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.