On Webster's Horn Equation
Erich S. Weibel · The Journal of the Acoustical Society of America · 1955
A wave equation for the sound propagation through tubes is derived by means of Hamilton's variational principle. It is assumed that the wave fronts can be approximated by surfaces of constant stream potential; this is the only assumption made. The variational principle ensures that the best equation that is compatible with this assumption will be obtained. The equation has the form of Webster's horn equation, however its coefficients are defined differently.