Instant accelelation in travelling wave

[petermer]

It just occurred to me: when a traveling wave approaches a certain point in the medium, the point remains still. When the wave reaches the point however, it instantly accelerates to maximum velocity. How does this happen? Where does this huge force come from? Is the time needed for the point to get this velocity negligible?

 

[torquil]

Are you referring to a discontinuous wavefront traveling through some medium? If so, that's probably just an approximation.

It could be a good appxorimation if you are only considering the system in question on such a large scale that the spread of the wave front can be regarded as zero.

Torquil

 

[mordechai9]

Yes, as torquil said, that's just an idealization... as the shock wave approaches the stationary atoms, there is a tremendous amount of microscopic collisional activity which very rapidly accelerates those atoms to the speed of the wave. The atoms in front of the wave don't feel the wave until it is already very close, because the wave is traveling faster than the ambient speed of pressure propagation. So there is no instantaneous acceleration, but the atoms are accelerated very rapidly at the last possible moment, and so it looks practically instantaneous from a macroscopic observer.

For an ordinary wave (equal to the sound speed), this dramatic acceleration doesn't occur, of course.

 

[petermer]

Ok, but how is this tremendous force generated from the atoms?