[Phys-L] pulse on a vertical rope

[mungan at USNA.EDU (Carl Mungan)]

d^2y/dt^2 = gx*d^2y/dx^2 + g*dy/dx

1. Why does the naive approach give such a close value for the time?

Okay, suppose I say d^2y/dx^2 scales something like dy/dx divided by
h, where h is the length of the pulse. (I'm assuming dispersion isn't
too large, since 10 returns of the pulse were observed.) Then clearly
the last term in the above equation is negligible for x >> h, which
is true over most of the length of the rope.

Okay, so I can see the answer to question 1.

But I'm still really interested in what can be said about question 2:
Can one solve the modified wave equation above for traveling
solutions exactly? If not, what can one say about it?
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
       U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5040
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