"Tom Donaly" wrote:

When you pluck a string, you are exciting the whole string at
once.

If a sound wave of the right frequency impinges on a string
perpendicular to the string's axis, the string will vibrate
sympathetically. In that case, it's hard to justify saying that
two waves are traveling in opposite directions up and down the
string.

OK, lets change the string. Now it's the top guy wire for a 1/4 wave
vertical at 560KHz. When you pluck it, you can hear it pinging as
the waves are reflected. Maybe it would be difficult to take that to
a symphony performance, but hey, true art is art no matter where you
find it

Nevertheless, the solution of the partial differential equation
describing the motion of the string, as proposed and solved by the
French mathematician D'Alembert, in 1747, is consistent with the
idea of two waves of arbitrary function traveling in opposite
directions on the string. If I were you, I'd find a copy of the
differential equation of a wave on a string and compare it to the
same equation describing an electromagnetic wave on a transmission
line. How similar are the two?

We may have lost the validity of the comparison to EM waves.

73,
Tom Donaly, KA6RUH

Regards,

Mike Monett