Energy Flow Criteria for Acoustic Propagation in Ducts with Flow

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Abstract
The propagation of sound in a rigid-wall rectangular duct is investigated for the purpose of determining the energy-transmission properties of the higher pressure modes. It is known in the case of ducts with no flow that for low frequencies these higher modes are cut off and transmit no energy. This phenomenon is easily recognizable in the wave-propagation solution by the appearance of purely imaginary wavenumbers. In ducts with a steady mean flow, the form of the solution for sound propagation is more complicated and the question of the direction of acoustic transmission is not clearly indicated. A complete investigation of this problem requires the use of the energy equation. This study uses forms of the energy density and energy flow vector in a uniform moving medium which are applicable for a linear theory of acoustic propagation. These relations are used in combination with the solution for sound propagation to identify the types of transmission which occur throughout the frequency range in a given mode of propagation.

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