Can the speed of sound reach the speed of light?

In summary, the equation for the speed of sound in air at a given temperature is v = (331.5 + 0.606T) m/sec, where T is in degrees Celsius. According to this equation, there is a theoretical temperature at which the speed of sound would reach the speed of light in a vacuum. However, this equation is only valid for a small range of temperatures and not at extreme temperatures such as the center of the Sun. Relativity also prohibits any sound from traveling at the speed of light. The speed of light in a vacuum is considered a "speed limit" for anything capable of transmitting energy or sending a signal. While it may be possible for the speed of sound to reach the speed of light
  • #1
michael3.1415
4
0
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?
 
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  • #2
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
Thanks for your reply! Two more questions:

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
michael3.1415 said:
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.
That 'speed limit' applies to anything capable of transmitting energy or sending a signal. (And it certainly applies to mass moving.)

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.
When we talk of nothing moving faster than the speed of light, we mean the speed of light in a vacuum.
 
  • #5
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
Doc Al said:
When we talk of nothing moving faster than the speed of light, we mean the speed of light in a vacuum.

So, it's theoretically possible for the speed of sound to reach the speed of light traveling through a medium?
 
  • #7
michael3.1415 said:
So, it's theoretically possible for the speed of sound to reach the speed of light traveling through a medium?
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
Ok thanks. I checked up the Cerenkov radiation thing. Very interesting.
 
  • #9
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

[tex]\sqrt{\frac{\gamma kT}{M}} = \sqrt{\frac{\gamma P}{\rho}}[/tex]

This is still based on classical physics, so this formula will also break down when the speeds and energies become relativistic.
 
  • #10
michael3.1415 said:
So, it's theoretically possible for the speed of sound to reach the speed of light traveling through a medium?

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
Beprepared said:
Sound can NEVER reach the speed of light in a vacuum...

I would love to see how you are going to measure speed of sound in vacuum :devil:
 
  • #12
Beprepared said:
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
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
Redbelly98 said:
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.

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

1. Can the speed of sound reach the speed of light?

No, the speed of sound cannot reach the speed of light. The speed of light, which is approximately 299,792,458 meters per second, is significantly faster than the speed of sound, which is around 343 meters per second in air. This is due to the different mediums in which sound and light travel, as well as the fundamental laws of physics.

2. Why is the speed of light faster than the speed of sound?

The speed of light is faster than the speed of sound because light travels through a vacuum, while sound requires a medium to travel through, such as air, water, or solid materials. The density and properties of these mediums affect the speed of sound, whereas the speed of light is a constant value in a vacuum according to Einstein's theory of relativity.

3. Is it possible to break the speed of sound barrier?

Yes, it is possible to break the speed of sound barrier, which is also known as Mach 1. However, this can only be achieved by objects such as supersonic aircraft or spacecraft that are designed and powered specifically to reach and sustain such high speeds. Breaking the speed of sound barrier is a significant achievement in the field of aeronautics and requires extensive engineering and design considerations.

4. Can sound travel faster than the speed of light?

No, sound cannot travel faster than the speed of light. As mentioned earlier, the speed of light is a constant value in a vacuum, while the speed of sound is dependent on the properties of the medium it travels through. Even in the densest medium, sound would still be significantly slower than the speed of light.

5. What happens when an object travels faster than the speed of sound?

When an object travels faster than the speed of sound, it creates a shock wave known as a sonic boom. This is a loud, explosive sound caused by the sudden increase in pressure and temperature as the object breaks the sound barrier. The intensity of the sonic boom depends on the size and shape of the object, as well as the speed at which it is traveling.

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