# Q & A: transverse and longitudinal sound in solids

Q:
When is the wave propagating in a solid transverse and when is it longitudinal? Because I've been taught that both kinds can propagate in a solid
- Annie (age 18)
NY
A:
You were taught correctly. (Followers of this site know that we rarely say that.) As for what type of wave is propagating in a particular case, that just depends on how the wave was generated.

Say that you hit a big steel block on top with a hammer. Just picturing how the atoms are displaced by the blow, you can see that there should be a compressional (longitudinal) wave going downward. Out to the sides, there should be transverse waves.

Mike W.

Life is even more complicated than that in the field of seismology.  Not only do transverse and longitudinal waves exist, called respectively s-waves (secondary) and p-waves (primary),  but there are several others which deal with surface phenomena.  See http://en.wikipedia.org/wiki/Seismic_wave for some interesting and gory details.

LeeH

(published on 03/30/2011)

## Follow-Up #1: sound wave momentum

Q:
Does transverse and longitudinal sound wave in solids carry any linear momentum and a net linear momentum? It looks like transverse sound wave carries no linear momentum along its traveling direction. Is this true? If so, why light wave which is transverse wave can (must always?) carry linear momentum along its traveling direction? Actually what would go wrong if a photon did not carry any momentum along its traveling direction? Could such a photon (without linear momentum) exist?
- Anonymous
A:

Yes, they do have momentum. You can see the momentum when it's exchanged, for example with electrons in the inelastic scattering events contributing to electrical resistivity or with phonons in Raman scattering. Everything obeys the universal quantum relation p=ħk, giving the quantum of momentum in terms of the wavevector.

Mike W.

(published on 08/25/2013)

## Follow-Up #2: momentum in waves

Q:
"Everything obeys the universal quantum relation p=ħk." Ok, this relation is applicable to photon, matter wave etc. (=everything?). But is this relation also universally applicable to "any wave" regardless of types:transverse and longitudinal wave, or sound, any mechanical wave like earth quakes, gravitational wave, surface wave in the sea etc.? They(=waves) all carry "momentum" which is determined by its frequency k multiplied by ħ? So, if you observe a wave, an object, or a system is "moving", it always carries "momentum."? Coming back to "transverse and longitudinal sound/mechanical wave" momentum: when sound wave enters a solid, say, a stone, the stone gains a bit momentum (pushed a bit? toward the sound wave propagation) and when sound wave leaves the stone, the stone loses a bit of momentum (recoils a bit (is pushed a bit to the opposite direction of the wave propagation))?? Sound can push or propel an object like a rocket?? Does a speaker start moving toward the opposite of its sound propagation with enough frequency and intensity(loudness)?
- Anonymous
A:

Q: "is this relation also universally applicable to any wave regardless of types"?

A: Yes, but now I've clarified above that it gives the size of the momentum quantum. The big waves you mention have huge numbers of quanta. If you compare that momentum quantum with the energy quantum you get the classical relation F=P/s, where F is the force exerted by the wave on the thing that's absorbing it, P is the power, i.e. rate of energy deposition, and s is the speed. If an extremely loud sound wave hits your whole body, say P=1 Watt, you get F=0.0003 Newton, equivalent to a weight of only about 30mg. So yes, sound can push an object, but the push typically is small.

Mike W.

(published on 08/29/2013)