Re: [Phys-l] waves on a string

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

Carl:

I wasn't familiar with equation 3 in the article to which you refer but
equation 4 makes sense.  It is consistent with the notion that each
infinitesimal bit of mass dm of the string is undergoing simple harmonic
moton so

dE = 1/2 k y^2 + 1/2 dm (dy/dt)^2

where k (determined by setting 1/2 k ymax^2 = 1/2 m vmax^2 where vmax =
2 pi f ymax) is given by

k = dm (2 pi f)^2

-------------

where:

k is the force constant of a ficticious spring that would provide a
force on the bit of string equal to the net force being exerted on the
bit of string by its neigboring string.

f is the frequency of the wave

-------------

I prefer writing his equation 4 as:

dE = 1/2 [mu dx (2 pi f)^2] y^2 + 1/2 (mu dx) (dy/dt)^2 

so it looks more like the energy 1/2 k x^2 + 1/2 m v^2 of a simple
harmonic oscillator but it amounts to the same thing.


> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of Carl Mungan
> Sent: Thursday, December 09, 2010 11:00 AM
> To: phys-l@carnot.physics.buffalo.edu
> Subject: [Phys-l] waves on a string
>
> In the past, we've discussed questions of energy and momentum
> transfer for waves on a string. (Try typing "Benumof" into the PHYS-L
> archive searcher for example.)
>
> 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.
>
> find this Letter near the bottom of: http://iopscience.iop.org/0143-
> 0807/31/5
>
> I wonder if some others on the list can look at this Letter and see
> what they think. -Carl
>
> --
> Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
> Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
> mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/
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