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Re: Wave Question



At 08:42 AM 9/12/99 +0800, you wrote:
----- Original Message -----
From: DEVARAKONDA VENKATA NARAYANA SARMA <narayana@HD1.DOT.NET.IN>
To: <PHYS-L@lists.nau.edu>
Sent: Saturday, September 11, 1999 4:23 PM
Subject: Re: Wave Question


At 05:59 PM 9/10/99 -0700, you wrote:
Perhaps we can also say that the intensity should always be calculated
from the resultant amplitude obtained by adding individual amplitudes
giving due consideration to the phase and not by adding individual
intensities.
Intensity should be always via amplitude.

regards,

sarma.

Calculating from the amplitude is well-established. But I was pondering
where the "extra" energy came from, and this has also been answered
qualitatively --- by looking at the whole system, i.e. while the energy has
doubled at constructive points, the energy is lowered on other points. But
how do we prove it more convincingly, maybe mathematically?

romanza


Perhaps this is what you want. Let us suppose that at some point
the waves that arrive are given by (taking the point under consideration
to be the origin)

y_1 = Asin(wt); y_2 = Asin(wt-phi)
The net displacement is ginen by
y = y_1 + y_2 = 2Asin{wt - (phi/2)}cos(phi/2) = {2Acos(phi/2)}sin(wt -
(phi/2))
The net amplitude is not 2A but 2Acos(phi/2). It is 2A only if phi = 2(pi)n
where n is an integer.

The Intensity
2 2 2

I = 2(pi) {2Acos(phi/2)} {w/2(pi)} v (rho)

where v is the speed of the waves and (rho) the density of the medium.
The derivation of above expression is available in most of the text books.

regards,

sarma.