Re: [Phys-L] Do waves ever transfer mass?

[John Denker <jsd@av8n.com>]

On 5/5/20 11:28 PM, Antti Savinainen via Phys-l wrote:

> I'm teaching an online HS course on waves. A bright student asked whether a
> wave ever transports mass. He referred to the model we are using which
> states that in a mechanical wave only energy moves, not mass (or the motion
> of mass is very limited, say, in a water wave). Does a tsunami make an
> exception? I quite understand what happens when a tsunami reaches the shore.
> However, a tsunami can travel a few hundred meters inland, even a couple of
> miles according to sources I read. This clearly is both transporting energy
> and mass. How would you recommend explaining this in terms of HS physics?

There are several different questions there, depending on
how we interpret the words.

The answer to most of them is "yes" but for several different
reasons.  Also, some of them are unanswerable.

For starters, we need to review the definition of "wave". The
typical HS textbook considers only sinusoidal waves, but in
the real world there are lots of other waveforms.  This is
directly relevant to the question that was asked, because
the area under a sine wave averages to zero, but for other
waves not necessarily.  The definition of "wave" is not at
all trivial:
  https://www.av8n.com/physics/wave-intro.htm

For example, if you pop a balloon, there is a sound wave
that propagates outward at the speed of sound.  But there
is also *air* that propagates outward.  This has fascinating
implications, because you cannot conserve energy *and*
conserve the number of air molecules (aka mass) at the same
time if the waveform stays the same.  Energy scales like
amplitude squared whereas the mass scales like plain old
amplitude.  So what started out as a simple step function
quickly develops wiggles.  This is why a nearby explosion
or lightning strike or gunfire sounds different (snap!)
from a far-away one (rumble-rumble-boom!).

Also we must distinguish transverse waves from longitudinal
waves.  It is as easy as π to have a longitudinal wave
transfer mass.  In fact it almost always does, unless you
go to great trouble to make the net area under the curve
of the waveform balance out to zero.  Example: balloon.
Example: Tsunami.

We must also distinguish the motion of the /medium/ from
the motion of the /wave/.  Suppose you speak to someone
who is upwind of you.  The medium is moving toward you,
even as the wave is moving toward them.

At the opposite extreme, we must also consider the case
where there is no medium, such as electromagnetism.
  --  An EM traveling wave is massless, but it carries
   energy and momentum.  The energy contributes to mass
   transport, but the momentum makes an equal-and-opposite
   contribution, so the net is zero.
  -- However, an EM /standing/ wave has mass.  In particular,
   a photon entering or leaving a region can change the
   amount of mass in the region, even though said photon
   is massless!  This is a not-so-subtle reminder that
   there is no law of conservation of mass, just conservation
   of energy and momentum, and mass is related NON-linearly
   to energy and momentum.  There is a diagram and some
   discussion here:
      https://www.av8n.com/physics/conservation-continuity.htm#fig-photons-in-boxes
   and here:
      https://www.av8n.com/physics/spacetime-welcome.htm#sec-invariance-conservation

   Asking whether the photon "transferred" mass in this case
   makes my head hurt. It's not a good way to frame the
   question or to understand the real physics.  Usually we
   apply the term /transfer/ to the transfer of a conserved
   quantity, and mass is not conserved.

There's a lot more that could be said, but I'll stop here.
I imagine there are gonna be follow-up questions.