Further observations on the anharmonic motion equation
作者:
J. R. Usher,
V. A. Nye†,
期刊:
International Journal of Mathematical Education in Science and Technology
(Taylor Available online 1989)
卷期:
Volume 20,
issue 3
页码: 399-406
ISSN:0020-739X
年代: 1989
DOI:10.1080/0020739890200308
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
Peters [1] discussed some theoretical aspects of the ‘ringing’ sound associated with barbershop quartet singing. These combination tones were first investigated theoretically by Helmholtz [2] who showed that the transient displacement of the ear membrane is governed by the anharmonic motion equation. Rayleigh [3] modelled the situation as an initial value problem and this is now referred to as the Rayleigh problem. Following [1] there has been a renewed interest in the problem (see [4‐8]). The intention of the present paper is to:alfaillustrate the qualitative behaviour of the solutions of the Rayleigh problem by a phase plane analysis;alfadescribe how the method of multiple scales provides a framework within which previous analyses can be seen;alfadescribe an improvement to the method of multiple scales, which may also prove useful in other applications.
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