Generalized Solutions of Webster's Horn Theory

Abstract

Webster's equation for the approximate formulation of the propagation of sound waves in horns is solved using two methods of approach. The first method considers a transmission line with variable parameters as the electrical analogue of the horn. This approach is specially useful in yielding generalized solutions for horns of finite length. The second method, based on an investigation of the singularities of Webster's differential equation, leads to the discovery of a great number of new families of horns.

Sound Absorbing Acoustic Horns

“…The theory of exponential horns has received considerable attention. 1 , [3][4][5][6][7][8] Other horn shapes have also been used such as conical, hyperbolic, or parabolic. Of them, the hyperbolic cosine type has often found application.…”

Approximate Results of Acoustic Impedance for a Cosine-Shaped Horn

“…Mawardi [7] has presented two approaches to solve the Webster equation, which consider an electrical analogue and the singularities of the di!erential equation. One technique which has been employed to solve this problem involves the partition of the horn into a number of conical-shaped elements, which together coincide approximately with the walls of the horn.…”

Distortionless wave propagation in inhomogeneous media and transmission lines

“…Some selected references relating to impedance transformation, filtering, signal dispersion and acoustics are given [4,5,6,7,8].…”