# Particle-wave duality of sound waves

1. Jul 1, 2010

### zewpals

I am extremely confused when it comes to particle-wave duality outside of the electromagnetic spectrum and quantum world. Are sound waves strictly waves or do they have "particle"-like aspects?

I understand that every particle has its own wave. Does this apply to every wave having a particle? Because it seems that any wave that requires a medium is strictly transfer of energy. Oh, maybe the energy is what makes up the particle. Haha E=mc^2. Did I just answer my own question or am I disillusion?

EDIT: Also, can radio waves, because they are so large, actually have a particle to be "found?" Thanks!

2. Jul 1, 2010

### graphene

Sound waves are mechanical waves. You have a sound wave because matter along the wave vibrates & this makes the wave propagate.

This is different from the case of EM waves where you talk about oscillating EM fields and photons.

The frequency of the wave does not matter, you would still have photons, but the energy of these photons depends on the frequency.

And yeah, you seem to be disillusioned about the transfer of energy & E=mc^2. You need an energy source to create a wave, like your vocal chords to create sound or electricity to 'create' light waves from a bulb. Then, these waves travel and carry the energy along with them.

3. Jul 1, 2010

### khemist

Particles do not have "waves," rather I believe they simply exhibit wave properties and particle properties, depending on the experiment done and depending if it is being observed or not.

And just as graphene said, sound is a pressure wave, where the particles in the air (the actual molecules, o2, n2, etc) vibrate to create sound. In space, where there are none of these macromolecules (I think that is the right term I should use) in the vacuum, sound cannot be created.

4. Jul 1, 2010

Would the particle aspect of a sound wave be considered a phonon?

5. Jul 1, 2010

### khemist

From what I understand, there is no particle aspect of a sound wave (other than the interaction of particles). The sound wave is created because there is movement OF particles, rather than something like light, where it is simply radiation emitted from a source.

I just looked at wikipedia, and I dont think a sound wave can be called a phonon, unless the sound wave is occurring in a lattice, which means that it is occurring in a solid.

6. Jul 1, 2010

### peteratcam

Sound waves travel through solids by causing the lattice to vibrate. Assuming harmonic (ie quadratic) interactions between the atoms, the dynamics of the lattice can be treated by studying the normal modes.

Classically, the energy in a normal mode can be anything.
Quantum mechanically, the energy changes in multiples of $$h \nu$$ where $$\nu$$ is the frequency of the mode.
Because the energy comes in lumps, all the same size, we call the lumps of energy 'a particle'. For a lattice, the particles are called phonons, for the em field, the particles are called photons.

It should be remembered that the illusion of particles comes from the peculiar fact that all energy levels are equally spaced in a quantum harmonic oscillator. Field particles don't exist outside of the quantum world : conversely, phonons in solids are as real as photons.

Pressure waves in a gas are a bit different though. khemist, the particles in a gas do not 'vibrate' to create sound. The gas is treated as a continuum fluid subject to thermodynamic expansion and rarefraction and the behaviour of the individual gas particles is pretty random. (To do that quantum mechanically, you'd need to learn about density modes in quantum liquids)

7. Jul 2, 2010

### f95toli

Yes, remember that sound in a solid IS just a lattice vibration. which -after quantization- is a phonon. Phonons can -under certain circumstances- have "quantum properties" that are very similar to what you would expect from conventional particlesö e.g. single phonon excitations of mechanical systems )such as a mechanical resonator) are more or less analogues to single photon excitation of EM systems (such as a microwave resonator) and it is also possible to couple single photons and phonons.

8. Jul 2, 2010

### ZapperZ

Staff Emeritus
As always, you may want to start by reading the FAQ thread in the General Physics forum.

Zz.

9. Jul 2, 2010

### Demystifier

10. Jul 2, 2010

### haael

You guys turned him down too early.

Mechanical waves also exhibit wave-particle duality. A "particle" is just a highly localized state. In the case of waves on water, it would be a drop, just hitting the surface. In the case of sound waves, it would be a small region of air with high pressure (the very moment of detonation, for instance).

Imagine "Dirac delta" state of gas pressure or water height. This would correspond to a detonation or a drop.

11. Jul 19, 2010

### zewpals

Hey guys, thank you for the answers that some of you provided. Sorry for not reading the FAQ's and checking previous forums. I'll do so for my next threads I want to start.

I've actually never heard of a phonon, but that's pretty cool =D. So I suppose since phonons have quantum properties, the wave-particle duality theorem still applies to sound waves. Thanks!

12. Jul 20, 2010

### Glen Bartusch

The reason why someone would want to avoid having to explain a particle/wave duality with something classical like the acoustic or water wave is because they're afraid to admit that they do not understand particle/wave duality among the E/M spectrum. They will say, "particle/wave dualities applies to quantum theory and not sound waves", but then they forget that nobody understands the particle/wave duality among the E/M spectrum!

It's OK guys. You can admit you don't know.

As for water or air being a "mecanical wave": last time I checked, light has a momentum which can push matter in historically classical ways, such as momentum from the light emitted by the sun pushing a solar kite, or momentum from the light in optical tweezers pushing large, heavy molecules along. Technically, this also makes light a "mechanical wave".

13. Jul 21, 2010

### vanhees71

I'm very willing to admit that I don't understand particle-wave duality. To put it more precisely, I don't know why one should think about a concept which is totally old-fashioned and unnecessary to think about for more than 80 years now! With the advent of modern quantum theory in 1925 (Heisenberg, Born, Jordan) and 1926 (Schrödinger, Dirac) this concept is obsolete.

Modern quantum theory is the basic theory underlying all physics and as such also sound waves, i.e., the collective vibrations of the crystal lattice in solids or density waves in liquids, gases and plasmas are perfectly well describable by quantum-many body theory.

The most simple approach is to use linear-response theory for a perturbation small compared to the intrinsic em. forces within the many-body system to calculate the retarded Green's function corresponding to the perturbation at hand, which of course is chosen such to probe the very phenomenon one is interested in. In the case of sound waves, you may excite a solid with a hammer or use some sound source (ideally a sine tone) to provoke the lattice vibrations or density waves. This is modelled in the theory by an appropriate external source coupled to the quantum fields used to describe the many-body system (usually assumed to be in equilibrium before the perturbation). Then one calculates the Green's function.

In energy-momentum representation, for a given momentum often these Green's functions show sharp resonance peaks at certain frequencies. In such cases of narrow resonances the Green's function resembles the Green's function of particles in vacuo, and that's why one can apply many techniques to these resonances known from vacuum quantum field theory, like Feynman diagrammatic perturbation theory, resummation techniques etc. etc.

That's why in such cases the collective modes of a many-body system are described in a very similar way as particles in the vacuum and thus often called "quasiparticles". Among other properties the most important one is that in the quasiparticle approximation the quasiparticles have a sharp dispersion relation $$\omega=\omega(\vec{k})$$ (or in quantum-theoretical language a sharp energy-momentum relation or "on-shell condition") like real particles in the vacuum. For sound waves, these quasiparticles are called phonons.

That's the only sense, I can make of the concept of "particle-wave duality" within modern quantum theory. Modern quantum theory is much less "esoteric" since it's the adequate description of the fact that there are neither classical particles nor classical fields (waves) but only quantum fields which connect these classical concepts to a coherent, however quite abstract, self-consistent scheme to describe the behavior of matter under any circumstances. Particularly also the classical behavior of macroscopic bodies becomes an emergent phenomenon to be described by approximations of quantum many-body theory.

14. Jul 21, 2010

### Pythagorean

In an acoustic wave, the wave is propagating through a medium. That is, there actually is particles involved, and their motion is what is wave-like. You can't have an acoustic wave without classical particles. Fundamentally, it's really no different than a vibration propagating through a string, or an s-wave from an earthquake traveling through the ground.

An electromagnetic wave, on the other hand, requires no classical particles. It propagates through space; there's no billiard-ball reaction of kinetics. The entire notion of a particle has changed with quantum mechanics; it just took human thinking a while to adjust. The truth is that the new definition of a particle doesn't match your intuitive idea of a particle.

The only reason the word 'wave' is in QM is because the fundamental equation has the same form as the wave equation in classical mechanics. In the classical regime, the wave equation describes the motion of particles. In QM, the concept of motion doesn't work the same way and the wave equation describe something different (but related) to the motion of the particle.

Even in classical EM theory, the wave equation has nothing to do with the position of any particles, but pertains to the value of the electric field intensity at a point in space. Such values exists at all parts along the wave simultaneously, so you can see it's quite a different kind of wave than the billiard-ball like domino effect of acoustics.

15. Jul 21, 2010

### mccoy1

16. Jul 21, 2010

### Plaster

Where is your evidence for particles ? You can have material detectors which are composed of particles that then detect a "particle" amount of energy and react to that level of energy by releasing an electron from their outer shell. Where is the evidence for EM itself being particulate ?

Last edited: Jul 21, 2010
17. Jul 21, 2010

### Plaster

Over 18 000 posts and thats the best you have to offer ? Do you hunger for the truth in these matters or do you believe we nearly understand everything, as Lord Kelvin did ?