The potential energy density in transverse string waves depends critically on longitudinal motion

Rowland, David R. (2011) The potential energy density in transverse string waves depends critically on longitudinal motion. European Journal of Physics, 32 6: 1475-1484.


Author Rowland, David R.
Title The potential energy density in transverse string waves depends critically on longitudinal motion
Journal name European Journal of Physics   Check publisher's open access policy
ISSN 0143-0807
1361-6404
Publication date 2011-11
Sub-type Article (original research)
DOI 10.1088/0143-0807/32/6/003
Volume 32
Issue 6
Start page 1475
End page 1484
Total pages 10
Collection year 2012
Language eng
Formatted abstract The question of the correct formula for the potential energy density in transverse waves on a taut string continues to attract attention (e.g. Burko 2010 Eur. J. Phys. 31 L71), and at least three different formulae can be found in the literature, with the classic text by Morse and Feshbach (Methods of Theoretical Physics pp 126–127) stating that the formula is inherently ambiguous. The purpose of this paper is to demonstrate that neither the standard expression nor the alternative proposed by Burko can be considered to be physically consistent, and that to obtain a formula free of physical inconsistencies and which also removes the ambiguity of Morse and Feshbach, the longitudinal motion of elements of the string needs to be taken into account, even though such motion can be neglected when deriving the linear transverse wave equation. Two derivations of the correct formula are sketched, one proceeding from a consideration of the amount of energy required to stretch a small segment of string when longitudinal displacements are considered, and the other from the full wave equation. The limits of the validity of the derived formulae are also discussed in detail.
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article # 003

Document type: Journal Article
Sub-type: Article (original research)
Collections: UQ staff Publications
Official 2012 Collection
 
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