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 [75], and it is an important component of the ``Leslie effect'' (described in §3.4.9).

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

$$\omega_l = \omega_s \frac{1+\frac{v_{ls}}{c}}{1-\frac{v_{s,l}}{c}} \protect$$ (4.6)

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, $v_{s,l}$ 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.