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#1 2006-03-04 04:45:17

John E. Franklin
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shinking sine

A typical sine wave will shink by 2 in x and y dimensions if squared.
See diagram.
But if the sine wave was a certain amplitude before it was squared it
would get bigger.
So there should exist an amplitude of a sine wave that when squared,
stays the same amplitude.
However, the wavelength will always continue to be halved.


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#2 2006-03-04 05:15:37

John E. Franklin
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Re: shinking sine

Oh yes, an amplitude of 2 which is a sine wave that varies from 2 to -2 in its height.
The two will square to 4, and the negative part of the wave will become positive, so the amplitude will be 2 again because it varies from 0 to 4 now, instead of -2 to 2.


igloo myrtilles fourmis
 

#3 2006-03-04 07:19:36

John E. Franklin
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Re: shinking sine

Also if you square a sine or cosine wave that is shifted up or down any amount, then the resulting shape is no longer a sine or cosine wave shape, it is misshapen.   I plotted a lot of examples to see this.
Also, the power reduction formula for sine and cosine say that the square of a sinewave is still a sinewave, but shifted in x and y, and half the size.   
One source says:      (sin x)^2 = (1 - cos (2x))/2


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#4 2006-03-04 07:37:56

krassi_holmz
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Re: shinking sine

, which is TRUE


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