Re: Wave Question

[Leigh Palmer <palmer@SFU.CA>]

> This is an interference question:
> Two coherent sources of equal amplitude are emitting waves in phase. At an
> equal distance away they superimposed at a point P, and hence it's
> constructive interference at P. By the Principle of Superposition, the
> amplitude at P is 2a.
> Since intensity is proportional to square of amplitude, the intensity at P
> is proportional to 4a^2. But the intensity of each wave at P is only a^2, so
> the "total" intensity is 2a^2. Intensity is the energy per unit area per
> unit time, so by conservation of energy, the intensity of the superimposed
> wave should be proportional to 2a^2, and from superposition principle, the
> intensity worked out to be 4a^2. So where has the other 2a^2 comes from? Pls
> enlighten.

You must look at the whole system. Energy is a system state function;
there is no reason to expect that it will be conserved locally. If you
consider the intensity which impinges on all the walls of the container
you will account for all of the energy radiated. After all, there are
also some places where the interference is destructive and the intensity
is nearly zero.

This brings me to another pet peeve. Why do we teach students about
the "intensity" of light when what we really mean is its *irradiance*.
The units tell it all; intensity has units of W/m^2 sr, while
irradiance (and also exitance) has the units we really mean, W/m^2 .

We really should clean up our act on this. Students get very confused
(and very wrong).

Leigh