Re: [Phys-l] waves on a string

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

If y = ymax cos[ (2pi/T)t + (2pi/lambda)x ]
then d^2y/dx^2 = -(2pi/lambda)^2 y
Substituting that and v = lambda f
into
- v^2 (d^2y/dx^2)
gives
(2 pi f)^2 y

> -----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 6:12 PM
> To: phys-l@carnot.physics.buffalo.edu
> Subject: Re: [Phys-l] waves on a string
>
> Jeffrey Schnick wrote:
>
> > 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.
>
> Are you really referring to Eq. (4)? In his paper it reads:
>
> dE = 1/2 (mu dx) (dy/dt)^2 - 1/2 (mu dx) v^2 y (d^2y/dx^2).
>
> His first term on the right corresponds to your second term, okay.
> But I don't see how his second term corresponds to your first term.
> How do you prove that:
>
> (2 pi f)^2 y = - v^2 (d^2y/dx^2) ?
>
> I don't see it. -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
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