NUMERICAL EXPERIMENTS ON ACOUSTIC RECIPROCITY IN COMPRESSIBLE POTENTIAL FLOWS IN DUCTS

✍ Scribed by W. EVERSMAN

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 340 KB
• Volume: 246
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2000.3609

✦ Synopsis

A reciprocity theorem for the scattering matrix for the propagation of acoustic modes in a duct with acoustically hard walls or with acoustically absorbing walls has been given in a companion publication. It was found that for a source at a speci"ed end of the duct, suitably scaled re#ection matrices in direct and reverse #ow have a reciprocal relationship. Scaled transmission matrices obtained for direct #ow and reversed #ow with simultaneous switching of source location from one end to the other also have a reciprocal relationship. A reverse #ow theorem for the equivalent one-dimensional propagation model, which is a good approximation to the three-dimensional model at low frequencies, was also obtained. In this case, using reciprocity and acoustic power conservation arguments it is additionally found that the acoustic power transmission coe$cient is the same for a source at either end of the duct for a given #ow direction. This result leads to an invariance theorem which relates acoustic power propagated due to sources of equal pressure amplitude at the two ends of the duct. A numerical veri"cation of these reciprocal relationships is given here for propagation in axially symmetric (circular and annular) ducts with multi-modal propagation and at low frequencies when a one-dimensional model is appropriate.