An extension of Shaw's theory to conical terminations : a new technique for muffler design



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Shaw's theory of sound propagation in acoustic horns with spatially varying density and elasticity is extended to conical terminations. The density variation technique was applied to simulate a conical termination in a tube of uniform cross section using perforated sheet-metal plates. The performance of the density variation horn and the equivalent conical horn was evaluated by comparison of the acoustic impedance and the acoustic pressure within the horns. It was observed that the density-variation conical horn had sound absorbing properties as a result of the use of the perforated plates to simulate density variation. Webster's equation is modified to account for the absorption of the medium. Expressions are developed for the acoustic pressure and the acoustic impedance taking into account the absorption of the medium. The theoretical calculations for the acoustic pressure and the acoustic impedance are in agreement with the experimental results of the density-variation conical horn. Due to the absorption properties of the density variation cone it can be used as a muffler. A prototype muffler was designed such that it would be suitable as an automobile muffler. The performance was evaluated using both a loudspeaker and an internal combustion engine as sound sources.