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.

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Subsections

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

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About the Author: 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.