On Jun 3, 12:51*am, Cecil Moore wrote:
On Jun 2, 11:48*am, K1TTT wrote:

my differential calculus is a bit rusty, but i don't think that
equation satisfies the basic wave equation.

My calculus is probably a lot rustier than yours but it would be very
important for this discussion if Maxwell's equations do not work for
the standing wave equation. That would essentially prove that the
mashed-potatoes theory of transmission line energy is bogus.
--
73, Cecil, w5dxp.com

well, i dug out mathcad that will do the ugly symbolic differentiation
for me. the standing wave equation can not satisfy the wave equation
derived from maxwell's equations as shown in either 'Fields and Waves
in Communications Electronics' section 1.14 or 'Classical
Electrodynamics' section 6.4. Both of them come down to the
requirement that the second derivative wrt space be proportional to
the second derivative wrt time. The proportionality constant is the
velocity squared. In order to satisfy this the equation must be a
function of the form F(t-x/v), the normal representation is the
complex exponential which can be presented in a form like sin(t)cos(x/
v)-cos(t)sin(x/v) the simpler standing wave equation sin(kx)sin(wt)
has the wrong relationship between space and time and therefor can't
be a solution to the wave equation. When i work through the second
derivatives and collect terms it results in something like
Asin(kx)sin(wt)(k^2-w^2) which makes no sense, even in a dimensional
analysis the units don't work.

The easiest explanation though is still the intuitive one, the
solution of the wave equation derived from maxwell's equations results
in the proportionality constant of 1/c^2 which requires the speed of
the wave to be c in the medium where it is evaluated, there is no way
to get that from the standing wave equation since it is obviously
stationary wrt space.