Open AccessOn the reflection of waves from a stratum of gradually varying properties, with application to sound
Author(s) -
J. W. G. Nicholson
Publication year - 1908
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1908.0082
Subject(s) - position (finance) , point (geometry) , reflection (computer programming) , variable (mathematics) , string (physics) , mathematical analysis , rayleigh wave , connection (principal bundle) , transverse plane , physics , mathematics , simple (philosophy) , classical mechanics , wave propagation , acoustics , optics , geometry , theoretical physics , computer science , engineering , philosophy , finance , structural engineering , epistemology , economics , programming language
In a variable medium, the velocity of propagation of a train of waves, and the wave-length at any point, are functions of the position of that point. The circumstances of such a propagation have only been worked out in detail in one particular case. Lord Rayleigh, in connection with the transverse vibrations of a string of variable density, dealt very completely with the case in which the density is inversely proportional to the distance from a fixed point. In his original investigation the results were applied to the corresponding optical problem, and a numerical example given. Although this is perhaps the only interesting case in which a simple exact solution appears possible, yet a close approximation may be made to the existing conditions, even in the general problem, when the waves are short in comparison with the other distances concerned. The development of such a theory, with an examination of some important cases, is the object of the present paper.