Instant accelelation in travelling wave

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Discussion Overview

The discussion centers on the behavior of a traveling wave as it approaches a point in a medium, particularly focusing on the acceleration of that point to maximum velocity upon the wave's arrival. Participants explore the nature of this acceleration, the forces involved, and the implications of wavefront propagation.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions how a point in the medium can instantaneously accelerate to maximum velocity when a traveling wave reaches it, and whether the force involved is significant.
  • Another participant suggests that the scenario may involve a discontinuous wavefront and notes that this could be an approximation, particularly if considering the system on a large scale.
  • A third participant elaborates that the situation described is an idealization, explaining that as a shock wave approaches, there is significant microscopic collisional activity that rapidly accelerates the atoms, making the acceleration appear instantaneous from a macroscopic perspective.
  • A participant seeks clarification on the source of the tremendous force generated from the atoms during this process.

Areas of Agreement / Disagreement

Participants express differing views on the nature of wave propagation and acceleration, with some suggesting idealizations and approximations while others provide explanations involving microscopic interactions. The discussion does not reach a consensus on the mechanisms at play.

Contextual Notes

The discussion includes assumptions about wavefront behavior and the scale of observation, which may influence interpretations of acceleration and force generation. The nature of the waves being discussed (e.g., shock waves versus ordinary waves) is also relevant but not fully resolved.

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

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