### ASA 126th Meeting Denver 1993 October 4-8

## 3aEA1. Rayleigh's horn equation.

**John T. Post
Elmer L. Hixson
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*Dept. of Elec. and Comput. Eng., Univ. of Texas, Austin, TX 78712
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Rayleigh's work on tapered waveguides is applied to acoustic horns. The
acoustic velocity potential is expanded in a perturbation-type solution and the
first perturbation is shown to produce the Webster horn equation on-axis, but
predicts progressive waves to have curved, or bulging, phase fronts.
Applicability of Rayleigh's first perturbation is shown to be identical to the
estimate given by Pierce for applicability of the Webster horn equation and
both of these reveal that the Webster equation cannot predict a ``cutoff''
frequency. When operating at the ``cutoff'' frequency predicted by Webster, any
practical horn is too short to load an acoustic source, so the performance is
virtually the same as letting the source radiate into free-space; but the horn
does not attenuate the progressive wave below the ``cutoff'' frequency in the
same way that high-order modes are attenuated below their cutoff frequency in
an acoustic waveguide. Rayleigh's second perturbation is presented as
``Rayleigh's horn equation.'' The acoustic impedance at the throat of the horn
and sound pressure interior to the horn as predicted from Rayleigh's theory are
compared with laboratory measurements.