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Chin. Phys. B, 2013, Vol. 22(5): 054301    DOI: 10.1088/1674-1056/22/5/054301

Benchmark solutions for sound propagation in an ideal wedge

Luo Wen-Yu (骆文于)a, Yang Chun-Mei (杨春梅)a b, Qin Ji-Xing (秦继兴)a b, Zhang Ren-He (张仁和)a
a State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China;
b University of Chinese Academy of Sciences, Beijing 100049, China
Abstract  Sound propagation in a wedge-shaped waveguide with perfectly reflecting boundaries is one of the few range-dependent problems with an analytical solution, and hence provides an ideal benchmark for a full two-way solution to the wave equation. An analytical solution for the sound propagation in an ideal wedge with a pressure-release bottom was presented by Buckingham and Tolstoy [Buckingham and Tolstoy 1990 J. Acoust. Soc. Am. 87 1511]. The ideal wedge problem with a rigid bottom is also of great importance in underwater acoustics. We present an analytical solution to the ideal wedge problem with a perfectly reflecting bottom, either rigid or pressure-release, which may be used to provide a means for investigating the sound field in depth-varying channels, and to establish the accuracy of numerical propagation models. Closed-form expressions for coupling matrices are also provided for the ideal waveguides characterized by a homogeneous water column bounded by perfectly reflecting boundaries. A comparison between the analytical solution and the numerical solution recently proposed by Luo et al. [Luo W Y, Yang C M and Zhang R H 2012 Chin. Phys. Lett. 29 014302] is also presented, through which the accuracy of this numerical model is illustrated.
Keywords:  coupled-mode theory      wedge-shaped waveguide      perfectly reflecting boundary      benchmark solution  
Received:  21 August 2012      Revised:  10 October 2012      Accepted manuscript online: 
PACS:  43.30.Bp (Normal mode propagation of sound in water)  
  43.30.Gv (Backscattering, echoes, and reverberation in water due to combinations of boundaries)  
  43.20.Fn (Scattering of acoustic waves)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11125420 and 10734100) and the Knowledge Innovation Program of the Chinese Academy of Sciences.
Corresponding Authors:  Luo Wen-Yu     E-mail:

Cite this article: 

Luo Wen-Yu (骆文于), Yang Chun-Mei (杨春梅), Qin Ji-Xing (秦继兴), Zhang Ren-He (张仁和) Benchmark solutions for sound propagation in an ideal wedge 2013 Chin. Phys. B 22 054301

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