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Old Mar 25th 2012, 12:42 PM   #1
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Amplitude and Intensity

My professor posted this:

$\displaystyle I = \langle \left| A(t) \right|^2 \rangle
= \int\limits_t \left| A(t) \right|^2 \, dt$

Since LaTeX doesn't seem to be working:

I = <|A(t)|^2> = Integral over t of |A(t)|^2 dt

OK, I can accept this relation between intensity and amplitude. But isn't there a 1/t factor missing to convert the integral sum to a mean average?

Or am I not understanding this? thanks!

Last edited by pramoda; Mar 25th 2012 at 01:03 PM.
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Old Mar 26th 2012, 10:55 AM   #2
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You're on the right track. The power of the wave is the average of the amplitude squared, or:

P = (1/T) Int (from 0 to 2 pi/w) A^2 dt

where T = period of the wave.

For a sine wave this works out to

P = 1/2 A^2

As for intensity - that is usually defined as power per unit area, so if you are d meters away from a source that radiates in all directions then intensity = (1/2) A^2/(4 pi d^2)
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