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Re: Energy Transmission on a string.



John M,
Thanks! I get the point now!
Your absolutely correct!! I see what you are getting at now!

I was making the very very silly mistake of computing the slope of
Cos(kx-wt) and not
A Cos(kx-wt).

I withdraw my objections to the standard derivations (of power and the wave
equation, see my response to John D.) in so far as its clear we are only
looking at "low amplitude" situations, which I fully admit is realistically
not much of a constraint for most vibrating strings our intro students come
across. I do think many authors should make this point more clear, that the
derivation is for small slope situations. (to be fair to Tipler, upon
re-reading I see he puts in that proviso.)

As Emily Latella would say:

Never Mind!

Joel

-----Original Message-----
From: John Mallinckrodt [mailto:ajmallinckro@CSUPOMONA.EDU]
Sent: Tuesday, December 04, 2001 12:04 PM
To: PHYS-L@lists.nau.edu
Subject: Re: Energy Transmission on a string.


Joel,

I think you are still missing the point. The maximumn angle of a
*perfectly* sinusoidal traveling wave with a wavelength of 1 m and
an amplitude of 1 cm is less than 4 degrees. And even this would
be an outrageously large angle for waves on a guitar string.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm

On Tue, 4 Dec 2001, RAUBER, JOEL wrote:

Given the constraint that it is truly sinsoidal, I don't
see a way to avoid
the fact that some mass elements along the curve have
slopes of 45 degrees,
which IMO would invalidate the use of the small angle
approximation (at
least for that region of the string).