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context: I have learned that mechanical waves can exist in all 3 dimensions, I was shown examples for each dimension of both longitudinal and transverse waves except for 1, which is the transverse wave in 3 dimensions.

Problem: I can't really imagine what a transverse wave in 3dimension looks like because even waves on the sea surface are just 2D waves, while explosions under the sea are 3-dimensional longitudinal waves, but can not seem to think of a 3D transverse wave. I tried google and can't seem to find an example either.

question: Could it be that all 3D mechanical waves are longitudinal? if not, can you provide an example or even an illustration of how a transverse wave would look in 3D?

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  • $\begingroup$ Press with high pressure a dense, viscous liquid into a rubber hose. It will make the hose expand as a 2D wavefront as it propagates through it along the third dimension. $\endgroup$
    – Steeven
    Nov 9, 2022 at 19:57
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    $\begingroup$ Earthquakes can produce transverse waves. See en.wikipedia.org/wiki/Transverse_wave $\endgroup$
    – Ghoster
    Nov 9, 2022 at 20:06
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    $\begingroup$ Phonons in solid materials have both longitudinal and transverse flavors. $\endgroup$
    – Jon Custer
    Nov 9, 2022 at 20:09

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As Jon mentioned in the comments, phonons in solids have transverse components. To elaborate, just as electromagnetic waves in a cavity are quantized, mechanical waves in a solid is quantized. The quantized modes are referred to as phonons (a pseudoparticle) just as the quantized modes of electromagnetic waves are called photons. They follow many similar properties as photons, such as the Planck distribution, and having transverse components. However, unlike photons, the possible number of phonons in the solid is bounded (see this answer on the stack exchange if you're not sure why).

If you are interested, you can look up the Debye theory of phonons; I believe Kittel & Kroemer has a section on it and shouldn't be hard to find at a library or through other means online.

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Just Realized that my answer is for 3D Longitudinal Wave and not for 3D Transverse Wave. (3D Longitudinal Wave are a good first step to be able visualize 3D Transverse Wave)

This is how I have been able to visualized Sperical Wave in hope it help others.

I started visualizing Sperical Wave when I have realised how sound work as our brain is naturally able to interpret sound which is propagating in sperical wave.

We know by instinct that if someone talk while being far away from us and not facing us :

  1. We will still hear this person. (This mean we know that sound don't go only straight forward but instead propagate in all direction like a sphere)
  2. The air going out of this person mouth is not dirrectly going into our ear, it is actually our Tympanic Membrane that vibrate and our brain that interpret this stimulus. (This mean that we know that Sound is pushing and pulling air to make our Tympanic Membrane vibrate)
  3. It will take time before we hear that sound. (This mean that we know that when you pull or push any material there is a delay before this mouvement reach the end "Phonon/propagation of a movement in any material is caused by the fact the you move only a group of atom that will propagate this mouvement to the following group". This mean that we know that mouvement of any material actually act like a wave)

From those 3 instinctive knowledge, we are now able to imaginate how the sound is Propagated as Sperical Wave that make our Tympanic Membrane vibrate.

Have an awesome day. Daniel Girard Bolduc

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