A New Fundamental Asymmetric Wave Equation and Its Application to Acoustic Wave Propagation

The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental the equation gives the most complete description of propagati...

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Bibliographic Details
Published in:Advances in mathematical physics 2023, Vol.2023, p.1-11
Main Author: Musielak, Z. E.
Format: Article
Language:English
Subjects:
Acoustic propagation
Acoustic properties
Acoustic waves
Acoustics
Asymmetry
Backward waves
Doppler effect
Eigenvalues
Mathematical analysis
Physics
Propagation
Wave equations
Wave propagation
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Summary:The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental the equation gives the most complete description of propagating waves as it accounts for the Doppler effect, forward and backward waves, and makes the wave speed to be the same in all inertial frames. To demonstrate these properties, the equation is applied to acoustic wave propagation in an isothermal atmosphere, and to determine Lamb’s cutoff frequency.
ISSN:1687-9120
1687-9139
DOI:10.1155/2023/5736419