shinking sine

John E. Franklin · 2006-03-03 05:45:17

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.

John E. Franklin · 2006-03-03 06:15:37

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.

John E. Franklin · 2006-03-03 08:19:36

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

krassi_holmz · 2006-03-03 08:37:56

, which is TRUE

Math Is Fun Forum

#1 2006-03-03 05:45:17

shinking sine

#2 2006-03-03 06:15:37

Re: shinking sine

#3 2006-03-03 08:19:36

Re: shinking sine

#4 2006-03-03 08:37:56

Re: shinking sine

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