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[Phys-L] Do waves ever transfer mass?


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?

Take care,

Antti Savinainen, PhD