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Re: [Phys-l] waves on a string




This ended up rattling around in my head, so I am going to share some thoughts with the list.
The first question is "why does the energy at each point have to be constant ?" It seems to me that all that is required is constancy of the total energy summed over the string.
Second, even with small amplitude, the length of any section of string varies, therefor there should be additional forces along the length of the string causing the mass density of the string to vary. This violates the elementary assumption that the tension in the string is constant. There ought to be a longitudinal standing density wave as well as the transverse wave.
Is this another case of trying to determine too much from a first order approximation ?
Al Bachman



Date: Thu, 9 Dec 2010 11:51:43 -0700
From: jsd@av8n.com
To: phys-l@carnot.physics.buffalo.edu
Subject: Re: [Phys-l] waves on a string

On 12/09/2010 09:00 AM, Carl Mungan wrote:
Anyhow, there's a recent Letter paper by Burko in Eur. J. Phys.
31:L71 (2010) claiming the usual textbook formula for energy of a
string wave is wrong. The gist is that instead of the square of dy/dx
in the PE term, one should have y * second deriv. of y w.r.t. x.

http://iopscience.iop.org/0143-0807/31/5/L01/

My first remark is that authors who don't number *all* of
their equations should be awarded a dunce cap or some other
badge of shame. It is spectacularly selfish for an author to
number only the equations /he/ wants to refer to. What if
somebody else wants to refer to some of the other equations?

My second remark is that Prof. Burko should proofread his
equations, and/or that IOP should find some reviewers who
actually look at the equations. Some of the equations in
this paper don't pass basic dimensional-analysis checks.

More importantly: I think the idea of the article is OK as
far as it goes. The author doesn't claim any originality
and cites Morse and Feschbach as a source of the approved
derivation.

I recommend that anybody who is interested in this stuff
(and almost everybody else) should take a look at what
Rayleigh had to say. That was one very smart guy, and
reading his book is always amusing.
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