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I knw it sounds dumb, but here is my problem. I can clearly imagine why amplitude has nothing to do with wavelength in a transversal wave, as they are measured along different axes in a graph. But in longitudinal, as particles vibrate along direction of wave propagation, wont twice the amplitude equal the wavelength? I m just comfused because both wavelength and amplitude are about to be measured along the same axis, unlike in transversal.

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The amplitude is related to the density of the medium. Here’s a gif that shows a longitudinal wave travelling. The amplitude in this case is maximum number of vertical lines within a unit frame.

enter image description here

And wavelength of course is the minimum (non-zero) distance between two places of same amplitude.

Image reference

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Amplitude is generally not a distance as such it is not true that the amplitude is twice the wavelength for longitudinal waves.

One way to convince yourself about this is to just think of a regular sound wave. The amplitude of the sound wave basically describes how dense the air is at a given point, more amplitude being related to having more density. On the other hand the wave length of said wave can be anything really as it depends on the frequency of the sound.

Another way to see how that would not work is to note that the amplitude of a sound wave decreases as the wave travels across space whereas its wavelength does not change much. This is why you stop hearing sounds if they are far away. If the amplitude were to be proportional to the wavelength then every sound would become high pitched as it disappeared and that is not what we see happen.

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