Re: wave momentum (reprise)

[Bob Sciamanda <trebor@VELOCITY.NET>]

In the May, 1999 AJP (arrived today) is :
D. Rowland and C Pask, "The missing wave momentum mystery", AJP, 67 (5), May
1999, pg 378-388.

Haven't read it yet, but I note that while the Benumof 1980 paper is not
cited, the Benumof 1982 paper is cited.
Check it out.

Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor


----- Original Message -----
From: Carl E. Mungan <cmungan@UWF.EDU>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Monday, April 19, 1999 6:53 PM
Subject: wave momentum (reprise)


> May I revive this topic? I have finally looked up the reference suggested
> by Bob Sciamanda:
>
> Reuben Benumof, "Simple harmonic motion in harmonic waves," AJP 48,
387-392
> (May 1980)
>
> and it is definitely an eye-opener!!!
>
> For light, we all know that the energy-momentum relation is E=cp. Reuben
> shows that EXACTLY the same relationship holds for mechanical waves, where
> E and p are now average (over either time or space) densities (eg. per
unit
> length for a wave on a string, per unit volume for sound, etc.) and c is
> the wave speed.
>
> So the answer to my original question is: all traveling waves do carry a
> nonzero average momentum. Hence, the Maxell ad, although wrong in
> magnitude, is right in principle: a sound wave will blow your hair back.
> You can calculate from the above relationship that the force should be
> experimentally verifiable for a decent stereo system - ie., I suggest
> dropping a feather in front of your speakers when the volume is cranked
and
> there are otherwise no drafts in your room and see if there is a net
drift.
> I haven't tried the experiment myself, but I'm dying to do so.
>
> This also means that a wave on a string is not simply transverse. There is
> a forward component. I think it's correct to think of this as the symmetry
> breaking phenomenon which drives the wave forward rather than backward,
> though I'd welcome comments on this interpretation.
>
> I also think we can carry Reuben's analysis a step further. Let's write
> p=mc where m is the net mass transmitted by the wave. Hence we have
E=mc^2.
> I think the reason this didn't come out as 0.5mc^2 is because the KE and
PE
> of any unit length (or volume) of the displaced medium are equal so that
> E=2*KE. I would then conclude that typical textbooks which state that
there
> is no bulk mass flow for a wave on a string, water surface, sound, etc are
> WRONG. (Of course, the wave must be traveling not standing, I hasten to
> add.) After all, this is what I usually do to elongate my garden hose when
> I'm too lazy to walk to the other end and tug on it.
>
> 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