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Exhaust noise of internal combustion engines is dominant at the engine firing frequency and the first few harmonics thereof. Therefore an efficient exhaust muffler is designed as wide-band low-pass acoustic filter. A simple expansion chamber (SEC) muffler would not satisfy this requirement because its transmission loss (TL) curve is characterized by periodic domes, with the troughs dipping to zero dB. As implied in the logarithmic addition, these low-frequency zero-dB troughs would result in drastic reduction in the overall insertion loss (IL) of the muffler. Therefore, during the last decade, tuned extended inlet/outlet chambers have been developed, where lengths of extended inlet/outlet are designed so as to tune out or cancel the troughs of the SEC muffler. These tuned configurations have been successful in that their TL curve is characterized by a single dome spanning over two (or four) consecutive domes of the corresponding SEC-TL curve, with the former standing a few dB higher than the latter. These features can only be explained by deriving an analytical expression for the TL-curve of a tuned muffler arranged in a form similar to that of the SEC muffler. This is what has been attempted here. In the present paper, an analytical expression has been derived for the TL curve of a tuned side-inlet axial-outlet (SIAO) muffler by means of electroacoustic analogies and transfer matrix method. This expression explains why the base TL curve of the tuned chamber is similar to that of the corresponding SEC with effective length reduced to half and area ratio increased to double. Consequently, one dome of the tuned chamber spans over two domes of the SEC-TL curve, and stands 6 dB higher than the TL-domes of the corresponding SEC.
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