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*From*: John Denker <jsd@av8n.com>*Date*: Wed, 6 May 2020 13:35:31 -0700

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.

**References**:**[Phys-L] Do waves ever transfer mass?***From:*<antti.j.savinainen@gmail.com>

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