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I'm trying to visualize how sound waves work and I was curious about something.

So sound moves in longitudinal waves, which I think I understand.

There is a really good khanacademy video explaining this.

In the video the air particles are depicted as moving from left to right (longitudinally). But do they ever move up and down even a little bit? Are they on some kind of fixed axis where they can only move longitudinally and never move even the slightest bit in a vertical direction?

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If you have any kind of solid material, it will become a little bit thicker as you compress it, and thinner as your stretch it. This means that a "one dimensional" wave traveling longitudinally down a rod will in fact cause some lateral motion. The ratio of displacements in the perpendicular direction is obtained from the strain (relative displacement of adjacent particles - how much local deformation there is) and the Poisson ratio of the material (a value between -1 and +0.5) that describes how much longitudinal strain turns into lateral strain.

So yes, it does move "the slightest bit".

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    $\begingroup$ Good basic qualitative explanation of shear waves. $\endgroup$
    – paisanco
    Jun 13, 2015 at 1:39
  • $\begingroup$ Here are some nice videos m.youtube.com/… $\endgroup$
    – Paul
    Jun 13, 2015 at 4:16
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    $\begingroup$ @Paul nice animations. The p-wave is closest to what I am describing but they don't really show the lateral displacement that follows. Still - it's a start. $\endgroup$
    – Floris
    Jun 13, 2015 at 14:58
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    $\begingroup$ @DanielGriscom I did say "traveling down a rod". Since there is no such thing as an infinite solid with an infinite plane wave, this is to some extent always true - even if only "the slightest bit" - which was the original question $\endgroup$
    – Floris
    Jun 13, 2015 at 18:18
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    $\begingroup$ Sound waves in air are pure "bulk" waves. If you approximate them as pure 1-D waves in an ideal gas, Poisson ratio does not come into it (except in the way it relates to the velocity of propagation - i.e. how soon you hear the sound after it is generated). Of course the mechanical mechanisms of detecting sound waves with the ear are extremely complicated, and involve sound traveling through solids and liquids. I hope that didn't confuse you more... $\endgroup$
    – Floris
    Jun 15, 2015 at 14:29
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That video is very poor in one aspect: particles in the sound field doesn't move "horizontally" nor "vertically". Really, the proper word is "longitudinal motion" and you are in fact asking about "transversal motion".

In basic description, the air is considered to be an ideal fluid. Therefore no shear stress is possible and hence no transversal motion as well.

In fact, there is a (little) viscosity of air, so yes, it's generally possible for particles to move a bit transversal as well. It could be observed especially in boundary layers on solid bodies. Of course, inside or on top of solid bodies or highly-viscous fluids, the transversal motion combined with longitudinal is natural.

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If we assume that you're talking about a broad sound wave traveling through a large, homogenous medium (air, water, rock) then normally, no: the pressure waves that are sound involve only motion along the direction of the sound's travel. You can wonder if the higher-pressure zones would tend to push the particles of the medium sideways, but remember that there's a broad area of higher pressure all traveling together, so that the only "escape" for the compressed particles is to continue the motion of the sound wave.

If you instead have a thin beam of sound, then it's likely that you'll get some form of lateral movement at the edges (probably related to the concept of diffraction, as in waves in the ocean diffracting around a point of land).

If you start dealing with non-homogenous media, then all bets are off.

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  • $\begingroup$ Shear waves can arise in homogeneous media as well. $\endgroup$
    – paisanco
    Jun 13, 2015 at 1:39
  • $\begingroup$ Sure, but what will stimulate them? If (as I was initially assuming) you have a broad wavefront, then any one particle will have the same conditions on either side, even as those conditions vary. So, there would be no lateral force, and no shear waves. $\endgroup$
    – Daniel Griscom
    Jun 13, 2015 at 11:33
  • $\begingroup$ Think of detonating a small charge buried in (assume it's homogeneous) rock. Is that going to produce a broad one dimensional displacement? No, it isn't. It will produce a spherical displacement with transverse and longitudinal components, and if the rock has nonzero shear modulus, the displacement excites both compressional and shear waves. $\endgroup$
    – paisanco
    Jun 13, 2015 at 20:10
  • $\begingroup$ (This isn't a great way to have a conversation, but...) OK, detonate a small charge within a large homogenous body of rock. The setup is spherically symmetric, and so will be the results. No lateral motion (where "lateral" is perpendicular to the local direction of travel of the shock). But, the initial question was about sound, with a specific interest in air-borne sound. So, detonate a small charge in a large homogenous body of air. Bingo: spherical shock wave, again with no lateral motion. $\endgroup$
    – Daniel Griscom
    Jun 13, 2015 at 22:47

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