Re: Wave Question

[DEVARAKONDA VENKATA NARAYANA SARMA <narayana@HD1.DOT.NET.IN>]

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.