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Descriptions of Sound Read chapter Read first chapter

2018 | OriginalPaper | Chapter

4. Principles and Equations for Multidimensional Phenomena

Author : Jerry H. Ginsberg

Published in: Acoustics-A Textbook for Engineers and Physicists

Publisher: Springer International Publishing

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Abstract

We will not analyze new phenomena in this chapter, nor will we develop new analytical techniques. Rather, our objective is to create the foundation for study of a variety of phenomena that do not fit the planar wave model. One possible difference is that the wavefront, which is the locus of points at which the acoustic disturbance was generated at a common time, is not planar.

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previous chapter Plane Waves: Frequency-Domain Solutions
next chapter Interface Phenomena for Planar Waves
Appendix
Available only for authorised users
Footnotes
1
Any velocity field can be represented in terms of a scalar potential function \(\phi \) and a solenoidal vector field \(\bar{\chi }\) according to \(\bar{v}=\nabla \phi +\nabla \times \bar{\chi }\). The circulation is \(\nabla \times \bar{v}\equiv \nabla \times \left( \nabla \times \bar{\chi }\right) \). The implication of neglecting viscosity is that it is not possible to induce circulation. Hence, the velocity potential may be used to represent the velocity field of any inviscid fluid, even in an analysis that includes nonlinear effects.
 
Metadata
Title
Principles and Equations for Multidimensional Phenomena
Author
Jerry H. Ginsberg
Copyright Year
2018
Book
Acoustics-A Textbook for Engineers and Physicists

Print ISBN: 978-3-319-56843-0

Electronic ISBN: 978-3-319-56844-7

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-56844-7_4

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