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# Re: Standing waves

The power formula in a textbook is derived
by integrating kinetic energy along one
lambda and then potential energy along one
lambda. The two are added and the sum is
divided by the period T. This gives

P=0.5*mu*w^2*A^2*v

where mu is mass per unit length, w is the
angular frequency, A is the amplitude and
v is the phase velocity. It is clear that mu
and v are constant. The relationship is
between three variables: P, w and A.

mu is predetermined by the string
v is imposed (caused) by tension and w is
imposed by the generator. What would be
wrong if somebody expected A to control
P and not P to control A? In other words, why
should power be the same as one goes
from a lower w to a higher w?
Ludwik Kowalski

On Monday, Feb 9, 2004, at 15:11 America/New_York, Vern Lindberg wrote:

My first thought is: Input power fixed by oscillator amplitude.

Power in wave for constant speed is proportional to n^2 y^2, therefore
at constant power the amplitude drops as 1/n.

On Monday, February 9, 2004, at 02:25 PM, Ludwik Kowalski wrote:

I think I found the answer shortly after
the send button was pressed. But is it
satisfactory (see below)?

For identical amplitudes the string would
have to be longer with 9 loops than with
one loop. For a rubber band (of low k) the
amplitudes would not be as different as
for a common string.

Dr. Vern Lindberg
585-475-2546
http://www.rit.edu/~vwlsps