On Sound Waves of Finite Amplitude

An analytical solution of Riemann’s equations for the one-dimensional propagation of sound waves of finite amplitude in a gas obeying the adiabatic law p = kργ is obtained for any value of the parameter γ. The solution is in the form of a complex integral involving an arbitrary function which is fou...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1953-02, Vol.216 (1127), p.539-547
Main Author: Copson, E. T.
Format: Article
Language:English
Subjects:
Amplitude
Analytic functions
Complex variables
Differential equations
Gas clouds
Integers
Mathematical independent variables
Partial differential equations
Sound waves
Waves
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An analytical solution of Riemann’s equations for the one-dimensional propagation of sound waves of finite amplitude in a gas obeying the adiabatic law p = kργ is obtained for any value of the parameter γ. The solution is in the form of a complex integral involving an arbitrary function which is found from the initial conditions by solving a generalization of Abel’s integral equation. The results are applied to the problem of the expansion of a gas cloud into a vacuum.
ISSN:1364-5021
0080-4630
1471-2946
2053-9169
DOI:10.1098/rspa.1953.0039