Wave speed vs. Speed of particles in medium

[km90]

This has always puzzled me and nobody (professors, textbooks) ever seemed to elaborate on it (maybe it is very simple and I merely didn't catch on).

Anyway, I understand that when a wave passes through a medium, the individual particles of the medium are briefly displaced from their equilibrium positions and then brought back to equilibrium by a restoring force (tension, gravity) unique to whatever the medium is (a string, the surface of a lake). Therefore the medium itself does not change position and the wave transfers only energy as it passes by.

So, my question is, is the speed at which the individual particles are displaced the same as the speed of the wave as it passes that particle (the particle moves a very small distance over a very small time, which turns out to be the same as the wave speed when calculated)? Or is it a totally different speed that is too difficult or too meaningless to bother calculating?

 

[QuantumPion]

They are related, but not the same. The position of a particle on the surface is governed by an equation of harmonic motion, such as y=A*sin(w*t) where A is the amplitude and w is the angular velocity (2*pi*frequency) of the wave. The velocity is the derivative of that equation, v=A*w*cos(w*t). I think the relationship might be more complicated for real water waves due to other forces at work though.

 

[astrokreng]

I can provide some insight into this question. The speed of a wave is determined by the properties of the medium through which it is traveling, such as density, elasticity, and tension. On the other hand, the speed of particles in the medium is determined by the individual properties of those particles, such as mass and the forces acting upon them.

In general, the speed of a wave is not the same as the speed of the individual particles in the medium. This is because the particles are not actually moving with the wave, but rather oscillating around their equilibrium positions as the wave passes through. Think of it like a line of people doing the wave at a sports game – the people are not actually moving down the line, but rather just standing up and sitting down in a sequential motion.

However, there are some cases where the speed of the particles in the medium can be related to the speed of the wave. For example, in a solid medium, the speed of sound waves is directly related to the speed of the particles, as they are tightly packed and can transmit energy quickly. In a gas, the speed of sound is not directly related to the speed of the particles, as they are more spread out and take longer to transmit energy.

So, to answer your question, the speed at which the individual particles are displaced is not necessarily the same as the speed of the wave. It is a different speed that is determined by the properties of the medium and the individual particles themselves. However, there may be cases where the two speeds are related, but this is not always the case and it is not typically a simple or meaningful calculation. I hope this helps to clarify some of the confusion surrounding wave speed and the speed of particles in a medium.