I Question about Waves -- What does "Elongation" refer to?

[math04]

What does it mean :g(x,t) which describes the elongation of the wave at the place x at time t. ? elongation what refer to exactlly!?

 

[davenn]

What does it mean :g(x,t) which describes the elongation of the wave at the place x at time t. ? elongation what refer to exactlly!?

to quote from
https://ncatlab.org/nlab/show/wave

In a mechanical system, the point in which the potential energy is minimal is called the equlibrium position; the relative position with respect to the equilibrium position is called the elongation. The maximal elongation is usually called the amplitude of oscillation.

 

[sophiecentaur]

"the relative position with respect to the equilibrium position is called the elongation".
@math04 The word 'elongation' (I don't like it at all) suggests to me that the context of that particular discussion is longitudinal waves and it describes motion 'backwards and forwards' in the direction of the direction of propagation. If you replace 'elongation' with the word 'displacement' then that takes care of any mechanical wave mode.

When you find a word that gives you problems, such as this one, it is always a good idea to read around. If you had done that then you would have found 'displacement' in pretty much every other discussion of waves.

 

[Cutter Ketch]

"the relative position with respect to the equilibrium position is called the elongation".

I not only don’t like it, I think it is flat out wrong. I took a brief look, and I can’t find elongation used as a synonym for displacement anywhere else. The dictionary definition is clear: the lengthening of something. In relation to oscillations, there is often a spring involved and elongation refers to the spring (or bond, or whatever) getting longer. In many simple 1D arrangements the elongation of the spring is equivalent to the displacement of the end of the spring or an attached mass so I can see how people conflate elongation with displacement, but those words do not mean the same thing.

Take, for example, a line of masses attached by springs supporting a transverse oscillation (passing pulse, continuous wave, standing wave, whatever). The displacement of the masses is transverse, and well described by the wave function. The elongation of the springs is easily calculable from the displacements and is not at all equal to the displacements. A perfectly good word with a pretty clear and well defined meaning, and it doesn’t mean displacement. It isn’t even correct for a longitudinal wave because the elongation of any spring will be the difference in the displacement of adjacent point masses.

Conflating these words because they happen to be equivalent in some circumstances strikes me as a grating malapropism.

None the less, I am not surprised and agree that they mean it to be synonymous with displacement. Horrible.