B What is the Quantum of Sound in Gases and Air

[ThunderLight]

It is usually referred to as Phonons for sound waves in solid. But, where it gets confusing, is in gases and air. Some still call it Phonons, others say, Phonons can only be used in solid states.

So what is the Quantum of Sound in Gases/Air?
And if possible, refer to any text which speaks of sound in gases as phonons or other. Thank you.

 

[John Park]

Since no one else has responded yet, I'll offer some thoughts, which may or may not be helpful.

Phonons are the basis of a quantum mechanical description of sound. As far as I can see, such a description is necessary or useful only when a classical description is inadequate--for example when individual phonons have energies appreciably greater than kT, so that only a few phonon states are occupied. Such a state would require very high frequencies (and short wavelengths), and I find it hard to imagine how it could occur in air or other gases, except under extreme laboratory conditions. The wavelength in a gas can't be less than the mean-free-path for collisions; this puts a limit on the wavelength (and therefore frequency) that can be achieved.

 

[mfb]

I don't see how you could get coherent (with the QM meaning) sound in a gas. Quantizing the motion of individual particles is possible in theory, but I would not call that "sound". I would expect the same issue with a liquid, unless it is very cold.

 

[John Park]

I don't see how you could get coherent (with the QM meaning) sound in a gas. Quantizing the motion of individual particles is possible in theory, but I would not call that "sound". I would expect the same issue with a liquid, unless it is very cold.

That sounds reasonable to me.

 

[hilbert2]

Doesn't a set of phonons behave like an ideal boson gas by itself? If it were possible to describe pressure waves in ideal gas with phonons, it seems to me as if you could then describe the behavior of the phonon gas itself with "higher order" phonons and so on, sorry if it's hard to see what I mean...

 

[mfb]

The boson gas of phonons doesn't have the right interactions to allow waves within this gas, as far as I know.

 

[vanhees71]

Hm, in a plasma you have excitations like plasmons (plasma oscillations), but I've never heard about phonons in a plasma or gas. I think they are defined as the quasi particles describing lattice vibrations for (crystalline) solids.

 

[mfb]

The plasma allows coherent long-range interactions.

 

[Demystifier]

I think they are defined as the quasi particles describing lattice vibrations for (crystalline) solids.

Exactly! A solid can be described as a series of coupled harmonic oscillators. Quantization of coupled harmonic oscillators leads to an equidistant spectrum, which is why it can be interpreted in terms of (quasi)particles. A liquid or gas is not so well described as a series of coupled harmonic oscillators.

 

[Vanadium 50]

Demystifier brings up a very good point - not all quantum systems lend themselves to description in terms of quasiparticles. Think about a particle in a box. The spectrum doesn't lend itself to adding things you can count. The n=2 state doesn't have twice of "something" that the n=1 state has.

 

[DrDu]

Sound waves in gasses and liquids are only observed in the hydrodynamic limit, i.e. when the free path length is much smaller than the wavelength of the soundwave. In principle, you can calculate them also quantum mechanically using either quantum Boltzmann equation or some Greens function formalism. The relevant quality is the density density correlation function or Greens function whose poles yield the dispersion relation for the sound waves. But in the hydrodynamic limit, all these exitations behave to a very good extent like classical harmonic oscillators which you can quantize using $E=(n+1/2)\hbar \Omega$.
The situation becomes much more interesting in superfluids and fermi gasses, where many new kinds of sound were predicted.

 

[Dr. Courtney]

Great discussion. Thanks for an insightful question and some very informative answers. Y'all make PF what it is!