Abstract
The exact solution to Webster’s differential equation for sound in an initial variable area duct is used to generate new families of duct shapes with their exact solutions. In most cases the shapes and their solutions may be expressed in terms of nth-order determinants (Wronskians, in fact) whose elements are solutions to the initial duct and derivatives of these solutions. The nth-order determinant contains 2n+1 arbitrary parameters which are available for the design of ducts. The initial duct may be any duct for which the solution to Webster’s equation is known. The method is applied to a uniform duct to derive new families of ducts where both the duct shape and its solution are expressed in closed form in terms of elementary functions. Special cases include filters, constrictions, and new horn shapes in addition to the well-known conical horn, Bessel horns, the exponential horn, the Salmon horn, and the sinusoidal duct. Subject Classification: 20.45; 85.60.
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