http://iet.metastore.ingenta.com
1887

## Acoustic scattering of a plane wave by a circular impedance cone

• Author(s):
• DOI:

£10.00
(plus tax if applicable)
10 chapters for £75.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:

Scattering of Wedges and Cones with Impedance Boundary Conditions — Recommend this title to your library

## Thank you

This chapter considers the diffraction of a plane acoustic wave illuminating completely the surface of a right-circular impedance cone. Formulation of the problem is also given for an arbitrary convex cone and uniqueness of the solution is discussed. By separating the radial variable the problem at hand is then reduced to that for a spectral function. Further separation of the angular variables for the circular cone leads to integral equations for the Fourier coefficients. The use of the Sommerfeld integral enables one to describe the far-field asymptotics for, in particular, the reflected wave, the spherical wave from the vertex of the cone, and the surface waves.

Chapter Contents:

• 5.1 Formulation of the problem and uniqueness
• 5.1.1 Formulation of the problem
• 5.1.2 On uniqueness of the classical solution
• 5.2 Kontorovich-Lebedev (KL) transform and incomplete separation of variables
• 5.2.1 Integral representation of the solution
• 5.2.2 Formulation of the problem for the spectral function u?
• 5.3 The boundary value problem for the spectral function u? (ω,ω0)
• 5.3.1 Separation of the angular variables for the circular cone
• 5.3.2 Study of the integral equation for R(?, n)
• 5.4 Diffraction coefficient in the oasis M for a narrow cone
• 5.4.1 Problems for the leading terms and for the first corrections
• 5.4.2 Calculation of V 1 and B 2j
• 5.4.3 Basic formula for the diffraction coefficient of the spherical wave from the vertex of a narrow cone
• 5.5 Numerical calculation of the diffraction coefficient in the oasis M
• 5.5.1 Numerical aspects
• 5.5.2 A perturbation series for ≫ 1
• 5.5.3 Examples
• 5.6 Sommerfeld-Malyuzhinets transform and analytic continuation
• 5.6.1 Analytic properties of Φtilde;(α, ω, ω0) and Φ(α, ω, ω0)
• 5.6.2 Problems for the Sommerfeld transformants
• 5.6.3 The singularity corresponding to the wave reflected from the conical surface
• 5.7 The reflected wave
• 5.8 Scattering diagram of the spherical wave from the vertex
• 5.9 Surface wave at axial incidence
• 5.9.1 Ray solution for the surface wave
• 5.9.2 Singularities of the Sommerfeld transformants corresponding to the surface wave
• 5.9.3 Asymptotic evaluation of the surface wave
• 5.10 Uniform asymptotics of the far field and the parabolic cylinder functions
• 5.11 Appendices
• 5.11.1 Appendix A
• 5.11.2 Appendix B. Reduction of integrals
• 5.11.3 Appendix C. Derivation of the constant C 0

Inspec keywords:

Preview this chapter:

Acoustic scattering of a plane wave by a circular impedance cone, Page 1 of 2

| /docserver/preview/fulltext/books/ew/sbew501e/SBEW501E_ch5-1.gif /docserver/preview/fulltext/books/ew/sbew501e/SBEW501E_ch5-2.gif

### Related content

content/books/10.1049/sbew501e_ch5
pub_keyword,iet_inspecKeyword,pub_concept
6
6
This is a required field