# Homework Help: Can the speed of sound reach the speed of light?

1. Jun 21, 2010

### michael3.1415

1. The equation given in my Physics text for the speed of sound through air at a given temperature

v = (331.5 + 0.606T) m/sec

where T is degrees Celsius

According to this equation, there is a theoretical temperature at which the speed of sound would reach c:

331.5 + 0.606T = c = 3.00 x 10^8 m/sec

331.5 is insignificant so: 3.00 x 10^8 m/sec = 0.606T and T = 4.95 x 10^8 degrees Celsius

The temperature at the center of the Sun is about 15 million degrees (1.5 x 10^7) so this is not ridiculously high.

Is this realistic, or is there a better equation for high temperatures? What would happen when this temperature is exceeded?

Last edited: Jun 21, 2010
2. Jun 21, 2010

### Staff: Mentor

That equation for the speed of sound as a function of temperature is only valid for a relatively small range of temperatures and under certain conditions. (Certainly not at solar interior temperatures!) I'm unable to give you a better equation for sound speed at those temperatures, but I can tell you that relativity will prohibit any sound from traveling at the speed of light.

Interesting question!

3. Jun 22, 2010

### michael3.1415

1. I'm not that familiar with relativity, but doesn't that rule only apply to matter? Sound is a wave like light. It's a wave propogated by the compression and rarefaction of actual matter, I guess, so that's probably the difference.

2. How exactly do you define the speed of light? Light speed varies. While sound speeds usually speeds up in denser mediums, light is inhibited by the existence of matter.

4. Jun 22, 2010

### Staff: Mentor

That 'speed limit' applies to anything capable of transmitting energy or sending a signal. (And it certainly applies to mass moving.)

When we talk of nothing moving faster than the speed of light, we mean the speed of light in a vacuum.

5. Jun 22, 2010

### Staff: Mentor

Sound is a longitudinal wave, when it propagates mass moves forward and back. So as the mass can't move faster than light, sound wave can't as well.

6. Jun 22, 2010

### michael3.1415

So, it's theoretically possible for the speed of sound to reach the speed of light travelling through a medium?

7. Jun 22, 2010

### Staff: Mentor

Beats me. But it's certainly possible (under the right conditions) to have a particle move through a substance faster than the speed of light in that substance. When a charged particle does this it can give off radiation. (Look up Cerenkov radiation.)

In any case, the relativistic 'speed limit' is the speed of light in a vacuum, not the (lower) speed of light in some medium.

8. Jun 23, 2010

### michael3.1415

Ok thanks. I checked up the Cerenkov radiation thing. Very interesting.

9. Jun 24, 2010

### dulrich

This link might help on the formula for the speed of sound:

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe3.html#c1

A "better" formula for the speed of sound (assuming air to be an ideal gas) is

$$\sqrt{\frac{\gamma kT}{M}} = \sqrt{\frac{\gamma P}{\rho}}$$

This is still based on classical physics, so this formula will also break down when the speeds and energies become relativistic.

10. Jun 24, 2010

### Beprepared

this one, i can answer... yes, sound can travel the speed of light AND FASTER

here's the caviat. I do not mean the speed of light in a vacuum. Light can be slowed. There are MULTIPLE experiments that have slowed it to 90 m/s or less...

the speed of sound is 340 m/s +/- a bit. And that's just in air... it's even faster in solids

Sound can NEVER reach the speed of light in a vacuum... it is as close to impossible as a thing can be.

Impossible just means really REALLY difficult. The word for a thing that can not happen is "contradiction" :)

11. Jun 24, 2010

### Staff: Mentor

I would love to see how you are going to measure speed of sound in vacuum

12. Jun 24, 2010

### Redbelly98

Staff Emeritus
But those experiments with slow speed of light were done using Bose Einstein condensates (assuming you are referring to the work of Lene Hau?), a pretty unusual state of matter. Is there a known measurement of the speed of sound in such a material? Just because the speed of sound is something in air, and even faster in solids, does not imply anything about what it is in a Bose Einstein condensate.

13. Jun 24, 2010

### Beprepared

very interesting point... i'd like to see info on that myself