Re: Waves

[James McLean <jmclean@CHEM.UCSD.EDU>]

"James W. Wheeler" wrote:
> Quick calculation for a transverse wave on a string.
>
> Let T= tension on the string.
> Let mu= mass per unit length of the string.
> Let the string lie along the x axis, and
> let the displacement of the wave be in the y direction.
>
> The energy density of the wave is then:
>         0.5*mu*(dy/dt)^2 + 0.5*T*(dy/dx)^2.
>
> The current of energy (flux) is:
>         -T*(dy/dt)*(dy/dx).
>
> Dividing this by the speed of the wave gives:
>         -sqrt(mu*T)*(dy/dt)*(dx/dt)
> which would be a momentum flux for the wave.
> (sqrt is the square root function)

Is this a typo?  Did you mean (using P for the second quantity)
P/v = P/ sqrt(T/mu) = -sqrt(mu*T)*(dydt)*(dy/dx)  ?

Why did you choose to divide by the velocity of the wave, rather than
the velocity of a point on the rope?

--
--James McLean
jmclean@chem.ucsd.edu
post doc
UC San Diego, Chemistry