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How unlike John!
Looks to me like you are mixing units.
Energy and amplitude may indeed be independent variables - though
usually not.
What I believe John has in mind is energy density or energy intensity
versus wave
amplitude at a spherical wave.
An Energy constant case:
mix a small boule of iron oxide and powdered aluminum: provide an
ignition source:
Constant energy, spherical wave: intensity as 1/r^2, amplitude as 1/r,
at the wavefront only.
A Power-constant case: a spark gap powered with a repetitive pulse
generator.
A constant power spherical wave, intensity as 1/r^2, amplitude as
1/r, for all radii in the far field.
...or not, as the case may be?
Brian W
On 6/27/2011 9:58 AM, John Mallinckrodt wrote:
Kyle,
It sounds to me like you are somehow trying to treat energy and amplitude as independent quantities. Fundamentally, it comes down to this: In the far field, the energy (per unit area) IS the amplitude squared. Thus, since E ~1/r^2, A ~ 1/r.
John Mallinckrodt
Cal Poly Pomona
The amplitude squared IS the energy.
On Jun 27, 2011, at 6:31 AM, Kyle Forinash wrote:
John;_______________________________________________
This has helped but I'm still confused. Even if energy (amplitude) were
constant we would expect energy per area to drop as 1/r^2 because the
sphere surface area is expanding. If the amplitude is also decreasing as
1/r then isn't the energy (amplitude squared) per area decreasing as 1/r^4?
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