A long time ago at Los Alamos I was part of a group involved in a
project to make detectors for aligning laser beams for laser fusion.
The detector was a 2-inch diameter wafer of silicon through which the IR
laser passed. Four electrical contacts were placed around the
perimeter. The laser pulse created a hot spot that propagated radially
from the point where the beam went through the wafer. If the four
contacts rose in temperature at the same time, the laser beam was
centered on the wafer. If the beam was not centered we could determine
its offset from center by the differing times of arrival of the thermal
"wavefront" at each of the four contacts.
We often referred to it as a circular wavefront, but we knew it was not
a wave. As Denker stated/implied, the moving temperature gradient
satisfies diffusion math and it does not satisfy the wave equation.
Indeed, we modeled the heat distribution as a gaussian centered on the
location of the beam. When we let this gaussian relax/change over time
it would become something like the form of
T(r,t)=(T_0/t)exp(-r^2/(t*sigma)). That is, time appears in the
denominator of the amplitude portion and multiplicative in the width
portion. The gaussian width increases and the amplitude decreases as
the thermal energy spreads out in the wafer. To satisfy the wave
equation, time needs to appear in the form r-vt, which it does not.
From a more qualitative viewpoint, I like to think that after a true
wave passes through a medium, the medium is restored to its pre-wave
condition. This is somewhat along the lines of some of Ludwik's
statements in his original post. As thermal energy spreads, the medium
behind the traveling front is not restored to its original condition; it
is hotter.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Chair of Sciences
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.