# Speed of sound

## Main Question or Discussion Point

I am wondering what density is required for a sound wave to travel at the speed of light (if possible at all!)
I'm not sure if there is a critical density at which a sound wave can go no faster.

Another related question is about 'cerenkov radiation': is it the same thing as light? That is, can we regard the waves of light to 'bunch up' in the same way as sound waves with a sonic boom?

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well, the speed of a sound wave depends not only on a density, but on the interaction between particles as well. I herad that theoreticians belived that at the BigBang the "sound" waves had the same speed as light. But, actually, that may be different physics altogether.
As to Chernkov radiation-this is an electromagnetic wave in a media. Because particles can travel with almost the speed of light, but electromagnetic radiation in a media shouldtravel with a fixed speed below the speed of light, we can have someting similar to sonic boom.

Gokul43201
Staff Emeritus
Gold Member
The speed of sound in a solid medium goes like the square root of E/d, where E is the elastic modulus, and d is the density. So, to make the speed of sound greater, you want the density to be lower (for a given E). However, it is not possible to substantially decrease d without decreasing E (or increase E without increasing d).

Think microscopically. To decrease d, you want to have a larger equilibrium spacing x between atoms. By increasing x, you are stretching out the potential energy (U vs. x) curve along the x-axis. The value of E goes like the second derivative d^2U/dx^2 or the curvature. By stretching out the PE curve along the x-axis, you are decreasing the curvature and hence the elastic modulus, E.

So, has anyone come with the idea to graph the speed of sound for different materials?

If what you say is true, and intuitively assuming that the elasticity modulus gets higher for denser materials, maybe an interesting relation can be established? (For instance, maybe when materials get too dense, the elasticity 'saturates', and thus the speed of sound decreases for even denser materials - implying that for better sound guidance you're best to opt for the 'break-even point'.)

Thanks for the replies.
Part of the question about sound is related to an article I read that (regarding the null aether result) in order for a vibration to travel at a rate equivalent to light, the density and tension of a material must be similar to that of steel.
Is this true?
Also I thought the rate at which vibrations proceed in a material is inversely proportional to the distance between atoms and how strongly they are binded (you can see vibrations travel faster in a tense wire than a tense string).

Mk
Symbreak said:
Thanks for the replies.
in order for a vibration to travel at a rate equivalent to light, the density and tension of a material must be similar to that of steel.
Is this true?
Do you think sound propagates at the speed of light through steel?

Temperature has a significant effect also, i.e. speed in air at zero deg.C = 332m/s; at +30deg. C = 349m/s.

Light in a vacuum travels at about 300k m/s. I think sound has a long way to go!

Astronuc
Staff Emeritus
Speed of sound would never reach the speed of light, since sound is the transmission of energy via collisions among atoms and the matter cannot travel at the speed of light.

Now, there is "Cherenkov" radiation (also spelled Cerenkov or Čerenkov) is electromagnetic radiation emitted when a charged particle passes through an insulator at a speed greater than that of light in the medium. [source Wikipedia - http://en.wikipedia.org/wiki/Cerenkov_radiation ]. Even though the speed of the particles is greater than speed of light in the medium (think index of refraction - http://en.wikipedia.org/wiki/Index_of_refraction), the rate at which the energy is dissipated by collisions is slower, and therefore the speed of sound is much slower than the speed of light.

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Astronuc said:
Speed of sound would never reach the speed of light, since sound is the transmission of energy via collisions among atoms and the matter cannot travel at the speed of light.

This means that there must be a critical limit where a sound wave can travel no faster. i.e if you get a really dense substance (perhaps like that found in the core of neutron stars) what is to prevent the sound vibrations approaching light speed? keep increasing density, tensions, temperature and so does the speed the vibrations propagate.
There is another situation where vibrations could travel 'instantaneously'; and that is, if there was a substance with no 'gaps' between the atoms, so the vibrations would not even be mediated! Obviously this is not physically viable but its an interesting thought experiment.

Gokul43201
Staff Emeritus
Gold Member
Symbreak said:
There is another situation where vibrations could travel 'instantaneously'; and that is, if there was a substance with no 'gaps' between the atoms, so the vibrations would not even be mediated! Obviously this is not physically viable but its an interesting thought experiment.
Even a thought experiment must be physical (meaning it should not violate known physics).

Describe to me, a pair of atoms without a 'gap'.

A shock wave, under special material arrangements, can be made to substantially increase its velocity. However, to my knowledge, the end result is far less than the speed of light.

Just a little reference about sound waves.
Sound vibrations travel through air at a speed of about 1,100f/s second. However sound vibrations travel faster through solid materials. The vibrations may travel over 10,000 f/s in soil, but in steel sound travels over 15,000f/s. The vibrations which produce sound travel as waves through air or other materials. The molecules of the surrounding materials respond to the vibrations as if the molecules were coils in a tiny spring and as the object vibrates, it makes molecules close to the object vibrate in the same pattern. The wave of vibration pushes against adjacent molecules and sets them in to motion. The molecules of the material do not move a great distance, sound waves spread through a material in circles. Since sound waves spread in all directions, the circles form a sphere of waves moving away from the vibrating source of sound. Sound waves require a material to move through; unlike light waves they can not move through empty space......
Galaxy..........

Physics Monkey
Homework Helper
Hi Symbreak,

There is one hyopethetical material that possesses the property that sound waves travel at the speed of light, and that material is old Lorentz ether. In order for light to be a vibration in such an ether, the ether would have to have some pretty fantastic mechanical properties, in particular it needs to very very very rigid. Much more rigid than steel, as others have noted! It has to have a lot of other strange and seemingly contradictory properties to properly account for light phenomenon. You can see from this thread that the ether clearly doesn't even come close to any material we know of on this Earth. Both because it seems unphysical and because it is superfluous (see Occam's Razor), modern physics has effectively discarded the old Lorentz ether concept.

Anyone know of experiments on sound through a Bose-Einstein condensate? Should be pretty fast.

Could a BEC be compressed?

Another stray thought; What would be speed of sound through a compressed plasma of quarks and gluons?

Mk
kublai said:
Anyone know of experiments on sound through a Bose-Einstein condensate? Should be pretty fast.
Could a BEC be compressed?
Well a BEC is kind of one particle, but I don't see why not?

Another stray thought; What would be speed of sound through a compressed plasma of quarks and gluons?

Gokul43201
Staff Emeritus
Gold Member
kublai said:
Anyone know of experiments on sound through a Bose-Einstein condensate? Should be pretty fast.
Why ? I'd think it would be extremely slow.

Could a BEC be compressed?
This is a more involved subject than you might have suspected. The compressibility of a BEC (~ $\partial n/\partial \mu$) has been studied theoretically (for several decades) and experimentally. Early models of the Bose gas predicted infinite compressibility - an unphysical result. It was only in the 1940's that this was resolved by Bogoliubov, with his quasiparticle approach for a weakly interacting Bose gas. However, this doesn't mean that you can arbitrarily increase the density of a BEC. Much to the contrary, most BECs are several orders of magnitude less dense than normal gases. There's a reason for this : the atoms that make up a BEC (whether it's helium or rubidium) are not really Bosons ! More correctly, they are approximately bosons. From a distance these atoms looks like bosons, but when you get close enough to be able to distinguish the individual fermionic components, you can no longer treat them like bosons. It is for this reason that a weakly interacting Bose gas is "weakly interacting" - and this interaction, can be approximated as a hard-sphere repulsion (it exists only below a certain separation). The upshot of all this is that you can not bring these bosonic atoms too close to each other (compress the BEC), lest they realize that they are not bosons after all.

Physics Monkey
Homework Helper
Hi kublai,

The speed of sound is actually quite low for condensates, of the order of a few mm/sec. In the Bogoliubov model, the speed of sound is given by $$c = \hbar \sqrt{4\pi a n }/m$$ (where a is the s-wave scattering length), thus the speed is small in part because the gas is so dilute. One reason why the gas has to be dilute is to supress the three body recombination rate. Three body recombination removes atoms from the condensate and so you want to minimize this rate to have long lived condensates. If the gas was too dense, then even if you could get condensation, the condensate would quickly die.

I'm afraid my conception of the compressibility of BEC is somewhat out of date. I rejected at once the idea of infinite compressibility but did consider cheek to cheek density a possibility. Probably because I always thought of zero terperature neing a cold, dead state (similar to deSitter state at end game). It now is obvious there is still a lot of energy at play at ~0kelvin, especially when considering condensates of Rb and similar metals.

Is the recombination rate very high in condensates of smaller atoms, less reactive elements than rubidium?

I wonder now about our definition of temperature, v.v. energy content.
:uhh: