Re: wave momentum

[James McLean <jmclean@CHEM.UCSD.EDU>]

"Rauber, Joel Phys" wrote:
> It was written:
> __________
> How about this:
> Take any wave supported by a (massive) medium, and which leaves the
> medium unchanged by it's passage.  That is, any piece of the medium ends
> up in the same position where it started, so that it's average velocity
> (and hence average momentum) is zero.  This in turn means that the
> momentum flux (which passed through the piece) must time average out to
> zero.
>
> Thus, an oscillatory wave through a massive medium cannot transmit net
> momentum.  (Sound transmits momentum *fluctuations*, but not *net*
> momentum.)  A domino or shock wave does transmit net momentum, because
> it doesn't leave the medium undisturbed.
> _________________________
> After the shock wave has passed, isn't the medium undisturbed.  This seems
> to be the case as the sonic boom passes through the air.  Same comment with
> respect to a wave pulse.

A wave pulse down a rope certainly does leave the medium undisturbed,
and therefore transmits no net momentum (although, again, it transmits a
momentum fluctuation).

For a true shock wave, the medium is disturbed.  For instance, with a
sonic boom there is a region of compressed air, but no region of
rarefied air (as there is in a normal sound wave).  Thus, as the boom
passes through the air, each little chunk of air ends up displaced from
its initial position.  Although the pressure, average velocity, etc. of
the air is the same afterwards as before, the position of each chunk has
changed, and hence it's average velocity (during passage of the boom)
was non-zero.

--
--James McLean
jmclean@chem.ucsd.edu
post doc
UC San Diego, Chemistry