[Phys-L] Re: pulse on a vertical rope

[mungan at USNA.EDU (Carl Mungan)]

John Denker replied:

>  > ps: It is not hard to find STANDING wave solutions to the above
> >  modified wave equation. If you substitute the trial form y =
> >  f(x)*cos(wt-d), you will get a solution where f(x) are Bessel
> >  functions of zero order.
>
> I think you've answered your own question.  Write it as
>    f(kx)*cos(wt-d)
> and solve for the dispersion relation, i.e. w as a function
> of k.  The general behavior will be a superposition of waves
> with different (w,k) values.

Yes, good, a Fourier series.

Can I make my work easier and construct my wave pulse shape as a
superposition of Bessel functions instead of sinusoids?
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
       U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5040
mailto:mungan@usna.edu       http://usna.edu/Users/physics/mungan/