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?

 

[PJC01]

Thank you for sharing your observation about traveling waves and their acceleration at certain points in the medium. This phenomenon is known as "wave acceleration" and is a well-studied concept in the field of wave mechanics.

To answer your question about where the force for this acceleration comes from, it is important to understand that a traveling wave is a disturbance that carries energy through a medium, but it does not carry any matter. This means that the wave itself does not exert a force on the point in the medium. Instead, the force that causes the point to accelerate comes from the medium itself.

As the wave approaches the point, it creates a buildup of energy in the medium. This energy is then released when the wave reaches the point, causing the point to accelerate to maximum velocity. This release of energy is what creates the force that accelerates the point.

As for the time needed for the point to reach this maximum velocity, it is not negligible, but it is very short. The exact amount of time will depend on the properties of the medium and the characteristics of the wave, but in most cases, it will be on the order of milliseconds or even microseconds.

I hope this explanation helps to clarify the concept of wave acceleration for you. If you are interested in learning more about this topic, I would recommend exploring the principles of wave mechanics and studying the mathematical equations that govern wave behavior in different mediums.