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The Herschel-Quincke tube: the attenuation conditions and their sensitivity to mean flow.

The classic Herschel-Quincke tube is a parallel connection of two ducts yielding multiple noise attenuation maxima via destructive interference. This problem has been discussed to different degrees by a number of authors over the years. This study returns to the basics of the system for the purpose of furthering the understanding of the conditions necessary for noise attenuation and especially their sensitivity to mean flow. First, the transmission loss for an N-duct system with mean flow and arbitrary conditions of state in the different ducts is derived. Next, the two types of conditions yielding the attenuation maxima are studied. In addition to a discussion of the underlying physics, generic expressions for frequencies at which maximum attenuation occur are presented. Experiments without mean flow generally show good agreement with theory based on straight duct elements. However, more detailed models may be required for accurate simulations in the presence of mean flow. A simple model compensating for the losses associated with bends is shown to improve the results significantly for the geometry studied.