Lossy Acoustic Propagation

Attenuation of waves by spherical spreading, as described in
§2.2.5 above, is not the only source of amplitude decay
in a traveling wave. In air, there is always significant additional
loss caused by *air absorption*. Air absorption varies with
frequency, with high frequencies usually being more attenuated than
low frequencies, as discussed in §B.7.15. Wave
propagation in *vibrating strings* undergoes an analogous
absorption loss, as does the propagation of nearly every other kind of
wave in the physical world. To simulate such propagation losses, we
can use a delay line in series with a nondispersive filter, as
illustrated in §2.2.2 above. In practice, the desired attenuation
at each frequency becomes the desired magnitude frequency-response of
the filter in Fig.2.4, and filter-design software
(typically matlab) is used to compute the filter coefficients to
approximate the desired frequency response in some optimal way. The
phase response may be linear, minimum, or left unconstrained when
damping-filter dispersion is not considered harmful. There is
typically a frequency-dependent weighting on the approximation error
corresponding to audio perceptual importance (*e.g.*, the weighting
is a simple example that increases accuracy at low frequencies).
Some filter-design methods are summarized in §8.6.

- Exponentially Decaying Traveling Waves
- Frequency-Dependent Air-Absorption Filtering
- Dispersive Traveling Waves
- Summary

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University