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*From*: Ludwik Kowalski <kowalskil@MAIL.MONTCLAIR.EDU>*Date*: Mon, 9 Feb 2004 16:00:44 -0500

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 afterDr. Vern Lindberg

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.

585-475-2546

http://www.rit.edu/~vwlsps

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