Small amplitude transverse waves on taut strings: exploring the significant effects of longitudinal motion on wave energy location and propagation

Rowland, David R. (2013) Small amplitude transverse waves on taut strings: exploring the significant effects of longitudinal motion on wave energy location and propagation. European Journal of Physics, 34 2: 225-245. doi:10.1088/0143-0807/34/2/225


Author Rowland, David R.
Title Small amplitude transverse waves on taut strings: exploring the significant effects of longitudinal motion on wave energy location and propagation
Journal name European Journal of Physics   Check publisher's open access policy
ISSN 0143-0807
1361-6404
Publication date 2013-03
Sub-type Article (original research)
DOI 10.1088/0143-0807/34/2/225
Open Access Status Not Open Access
Volume 34
Issue 2
Start page 225
End page 245
Total pages 21
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2014
Language eng
Abstract Introductory discussions of energy transport due to transverse waves on taut strings universally assume that the effects of longitudinal motion can be neglected, but this assumption is not even approximately valid unless the string is idealized to have a zero relaxed length, a requirement approximately met by the slinky spring. While making this additional idealization is probably the best approach to take when discussing waves on strings at the introductory level, for intermediate to advanced undergraduate classes in continuum mechanics and general wave phenomena where somewhat more realistic models of strings can be investigated, this paper makes the following contributions. First, various approaches to deriving the general energy continuity equation are critiqued and it is argued that the standard continuum mechanics approach to deriving such equations is the best because it leads to a conceptually clear, relatively simple derivation which provides a unique answer of greatest generality. In addition, a straightforward algorithm for calculating the transverse and longitudinal waves generated when a string is driven at one end is presented and used to investigate a cos2 transverse pulse. This example illustrates much important physics regarding energy transport in strings and allows the ‘attack waves’ observed when strings in musical instruments are struck or plucked to be approximately modelled and analysed algebraically. Regarding the ongoing debate as to whether the potential energy density in a string can be uniquely defined, it is shown by coupling an external energy source to a string that a suggested alternative formula for potential energy density requires an unphysical potential energy to be ascribed to the source for overall energy to be conserved and so cannot be considered to be physically valid.
Keyword Dimensional linear waves
Damped free-vibration
Piano strings
Momentum
Length
Field
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: UQ staff Publications
Official 2014 Collection
 
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