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



generality
would require k to be a complex function of x. The imaginary part is
needed because of the first derivative in the MWE and gives rise to
dissipation (damping).

I've been thinking some more about this point and realize I'm
confused about this important matter also.

On the one hand, as the pulse goes up the string, it speeds up. This
will cause its amplitude y to decrease even without damping. It's
like the tsunami, which in fast deep water is only 1 foot high, but
piles up into a tall wave when it slows down near the coast. The
front of the pulse rushes forward, the rear of the pulse lags. But
later when the pulse goes back down the rope, it will mostly
reconstitute itself, thus explaining why experimentally (from the
previous reference I gave), up to 10 returns of the pulse were
observed.

But, even absent air drag, nonidealities of the string, and a loose
attachment to the top point, I still think the pulse will suffer some
dissipation. As it speeds up, it's like a light pulse passing from
one refractive index zone to another. Hence there will be some
reflection losses everywhere along the length of the whole string.
Soon the whole string will be wiggling and you'll no longer have a
coherent wave pulse, right?

Does the imaginary part of k include both of these effects (change in
y as wave spreads out without loss, and loss in energy of the pulse
due to continuous reflection impedance mismatch)?
--
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/
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