John T. Post Elmer L. Hixson
Dept. of Elec. and Comput. Eng., Univ. of Texas, Austin, TX 78712
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.