Carl,
I suggest that you look at p.359 of Griffiths' "Intro to
Electrodynamics". The momentum density, p', is equal to 1/c^2 * S where
S is the Poynting vector. There is more on this in the book and it is
impossible to type it all here. Oh yeah, this is for a electromagnetic
wave so I am not quite sure this answer your question. But I assume you
make analogies to the mechanical waves by the fact that a mechanical
wave is energy propagating by medium disturbance (E&M are only different
in that they have a fixed velocity in vacuum of c and need no medium).
Hope that helps because I am now convinced it may not. Oh well, maybe I
will do better next time.
Sam Held
-----Original Message-----
From: Carl E. Mungan [mailto:cmungan@UWF.EDU]
Sent: Wednesday, March 10, 1999 6:54 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: wave momentum
Under what conditions can a wave be said to carry momentum? Defining
momentum as the time integral of a force, light carries momentum, which
manifests itself as an electromagnetic force on a surface it reflects
off
of. We can understand this purely classically by considering the
electric
and magnetic fields interacting with a surface electron.
We can also get the momentum quantum mechanically (QM) from p =
h/lambda.
Finally, from special relativity (SR) we could invoke "relativistic
mass" m
and correctly get it from E = mc^2 and p = mv (with v = c) so that p =
E*v/c^2 (= E/c for photons).
The QM and SR relations also give the correct momentum for a massive
particle such as an electron, where v is now its speed and lambda its de
Broglie wavelength.
But what about mechanical waves? For phonons, h/lambda gives the
"crystal"
momentum, but that's not a true momentum in the sense of exerting a
force,
I'm told. Is there any meaning to the quantity E*v/c^2 where v is the
phonon speed of sound and E = h*nu?
Intuitively it seems a mechanical wave doesn't carry momentum since
there's
no mass flow. A cork on the surface of the sea just bobs up and down
(okay,
the bobbing is slightly circular, but never mind that). I assume surfing
requires interaction with the drag force from the sea bottom near the
beach
as the wave breaks, so that still doesn't necessarily mean a water wave
carries momentum.
Comments? Carl
Dr. Carl E. Mungan, Assistant Professor http://www.uwf.edu/~cmungan/
Dept. of Physics, University of West Florida, Pensacola, FL 32514-5751
office: 850-474-2645 (secretary -2267, FAX -3323) email: cmungan@uwf.edu