Abstract
Our attention now turns to situations where a plane wave propagates obliquely relative to a planar interface with another medium. The consequence will be a wave that is somewhat different from the one encountered in a one-dimensional waveguide. A wave might also be transferred into the receiving medium. The analyses will employ Cartesian coordinates aligned with the boundary to describe the multidimensional phenomena. Each topic is important for a variety of applications, such as noise control for wall design. Each topic represents an advance toward our goal of fully understanding how acoustical waves behave.
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Notes
- 1.
A. Sommerfeld, “A Green’s Function of the Oscillation Equation,” Jahresber. Dtsch. Math. Ver. 21, 309–353 (1912).
- 2.
In many texts, one will find that the expression for R is the form obtained when the numerator and denominator of Eq. (5.2.8) are multiplied by \(\cos \psi _{1}.\) The form used here is chosen for consistency with the next section, wherein the interaction between two fluids is investigated.
- 3.
A comprehensive presentation of analytical solutions may be found in the recent text by C. Y. Yang and C. M Yang, Structural Vibration: Exact Solutions for Strings, Membranes, Beams, and Plates, CRC Press (2013).
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Ginsberg, J.H. (2018). Interface Phenomena for Planar Waves. In: Acoustics-A Textbook for Engineers and Physicists. Springer, Cham. https://doi.org/10.1007/978-3-319-56844-7_5
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DOI: https://doi.org/10.1007/978-3-319-56844-7_5
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