Speed of Light & Sound: Revolutionary Phenomenon?

[geordief]

Again, you are completely missing the revolutionary part. The revolutionary part is not that c was independent of the speed of the emitter (even sound waves do that) but that it was the same in all inertial frames.

It makes no sense whatsoever to claim that something is not revolutionary by ignoring the revolutionary part! Do you also measure the brightness of the sun by putting your sensor in the shade?

If sound (or any wave) was transmitted in a medium whose density was vanishingly low , would that wave propagate in the same way as em radiation in a vacuum?

And vice versa does em radiation propagate in the same way as ,say sound so long as it is in a dense enough medium?

In other words is it the vacuum that is instrumental in the phenomenon that is the invaiance of the speed of light,?

 

[Dale]

If sound (or any wave) was transmitted in a medium whose density was vanishingly low , would that wave propagate in the same way as em radiation in a vacuum?

I guess you are thinking of the formula for the speed of sound: $\sqrt{B/\rho}$. But as $\rho \rightarrow 0$ we also have $B \rightarrow 0$ so I don’t know what the limit is.

 

[geordief]

I guess you are thinking of the formula for the speed of sound: $\sqrt{B/\rho}$. But as $\rho \rightarrow 0$ we also have $B \rightarrow 0$ so I don’t know what the limit is.

I assume that your speed of sound formula takes no account of relativity.

I also assume that there is no practical need for any such formula as relativistic effects never arise in any normal situation .

Am I also right to assume that ,between sound waves and em waves there are no examples of waves that propagate faster than the former and slower than the latter?

 

[Dale]

I assume that your speed of sound formula takes no account of relativity.

Sorry, I assumed that was the formula you were referring to above. Please clarify what formula you intended by:

If sound (or any wave) was transmitted in a medium whose density was vanishingly low , would that wave propagate in the same way as em radiation in a vacuum?

If not the above formula, then what would lead you to suggest this?

 

[geordief]

Sorry, I assumed that was the formula you were referring to above. Please clarify what formula you intended by: If not the above formula, then what would lead you to suggest this?

I didn't have a formula in mind as I lack that education.

I was just responding to your observation that the formula you provided seems to be undefined when the conditions approach that of a vacuum.

Unsurprising I suppose as sound is said to not propagate in a vacuum.

Is em radiation the only kind wave that can transmit in a vacuum?

I wonder what are the actual upper and lower limits of the speed of sound in a medium?

Perhaps ,if I am off topic I should start a separate thread?

 

[Dale]

Perhaps ,if I am off topic I should start a separate thread?

Good idea. I have moved it.

 

[Nugatory]

Is em radiation the only kind wave that can transmit in a vacuum?

Gravitational waves also propagate through a vacuum.

I wonder what are the actual upper and lower limits of the speed of sound in a medium?

The speed of sound in a homogeneous medium is determined by the ratio between its stiffness and its density: it increases with stiffness and decreases with density. It's easy to find materials in which the speed of sound is near as never mind zero. In principle there could be materials in which the speed of sound is very close to $c$, but in practice even the lightest stiffest materials known don't come close.

 

[Dale]

I was just responding to your observation that the formula you provided seems to be undefined when the conditions approach that of a vacuum.

Now I am getting really confused. You cannot have been responding to my formula in your first post because the formula came after your first post.

So again, please clarify. In your first post here, what led you to suggest this?

If sound (or any wave) was transmitted in a medium whose density was vanishingly low , would that wave propagate in the same way as em radiation in a vacuum?

 

[PeroK]

If sound (or any wave) was transmitted in a medium whose density was vanishingly low , would that wave propagate in the same way as em radiation in a vacuum?

I feel like you are looking at this the wrong way. Sound is an oscillation of a physical medium: air, for example. The concept of sound can only make sense if the medium is sufficiently dense. If you only have three air molecules in a room, you effectively have a vacuum and there are simply not enough air molecules to support the concept of sound.

Sound requires a huge number of particles before you can identify the macroscopic concept of a sound wave.

It's difficult to see why there would be a connection between the behaviour of a few scattered air molecules and electromagnetic radiation. That question suggests you are not thinking clearly about these things.

 

[geordief]

Now I am getting really confused. You cannot have been responding to my formula in your first post because the formula came after your first post.

So again, please clarify. In your first post here, what led you to suggest this?

Well ,it was in my mind that it might be the nature of the vacuum that was responsible for the fact that the speed of light was invariant.

I knew that sound waves also propagated in such a way that their speed was independent of the motion of the frame of reference whence they were emitted and I was trying to puzzle out whether ,by rarifying the density of the medium they propagated in the property of the sound wave would be identical to that of light.

I think I have learned that in principle the speed of sound can approach c but cannot be invariant as it depends on a medium for its very existence (Is actually a phenomenon of the medium)

Hope I have explained "what led me to suggest this"

Btw are gravitational waves invariant in the same way as light?

 

[Nugatory]

Btw are gravitational waves invariant in the same way as light?

Yes

 

[Meir Achuz]

Maybe I missed it, but I do not see Einstein's 1905 statement about the speed of light posted, so I will do that here: "...and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."
I don't know why he mentioned the speed of motion of the emitting body, but it does make it look a lot like the speed of sound

 

[Ibix]

I don't know why he mentioned the speed of motion of the emitting body, but it does make it look a lot like the speed of sound

I think he's distinguishing his theory from both ether theory, where the speed of light is $c$ relative to the ether, and ballistic theory, where the speed of light is $c$ relative to the emitter.

 

[geordief]

In principle there could be materials in which the speed of sound is very close to c, but in practice even the lightest stiffest materials known don't come close.

In that hypothetical scenario would the property of the sound wave propagation "approach invariance"in any measurable way?

 

[Halc]

In that hypothetical scenario would the property of the sound wave propagation "approach invariance"in any measurable way?

It would seem so. If I had a material moving at .8c to the left in my frame, sound moving to the right in it (or to the left for that matter) would move at nearly c in my frame, assuming speed of sound in the material was very close to c.

If speed of sound in a stationary material is .99990c and the material moved at .8c in my frame, then the sound would move at .99910c against the motion and at .99999c in the other.

 

[geordief]

It would seem so. If I had a material moving at .8c to the left in my frame, sound moving to the right in it (or to the left for that matter) would move at nearly c in my frame, assuming speed of sound in the material was very close to c.

But ,since as density increased movement of the molecules or particles would be more and more difficult the amplitude of the propagation of any sound wave would approach zero.

Does that also sound right?

EDIT: Think I should have said "as stiffness increases and density decreases" so my point seems shaky now...

 

[Dale]

Well ,it was in my mind that it might be the nature of the vacuum that was responsible for the fact that the speed of light was invariant.

Thanks, that helps. I think that is correct in principle. The only thing is that sound waves don't go through vacuum, but any wave that does go through vacuum would need to travel at c.

 

[geordief]

Thanks, that helps. I think that is correct in principle. The only thing is that sound waves don't go through vacuum, but any wave that does go through vacuum would need to travel at c.

For those waves that do travel through a vacuum,would it be correct (or as an interpretation) that they travel through a field?

If so ,can this field be construed as a physical object or is it to be understood as the set of all possible measurements of a test particle in the region in question?

 

[geordief]

If speed of sound in a stationary material is .99990c and the material moved at .8c in my frame, then the sound would move at .99910c against the motion and at .99999c in the other.

Yes ,that was what I was wondering. Are there any implications to that ? It seems invariant in all but name ,even though it seems an impossible scenario.

 

[Halc]

It seems invariant in all but name ,even though it seems an impossible scenario.

But it's not invariant at all. That's just how velocity addition works with super fast speeds.

With real materials it is different. Sound moves through air at 340 m/sec and in any frame other than that of the air, you add the frame speed to that (just like my superfast example above). So if you're moving at 500 m/sec, that's supersonic and it is impossible to hear anything behind you. That is a very frame dependent property, not just in name at all.

 

[PeroK]

Yes ,that was what I was wondering. Are there any implications to that ? It seems invariant in all but name ,even though it seems an impossible scenario.

In a frame moving at an appropriate velocity, the speed of the sound wave would be zero.

 

[geordief]

But it's not invariant at all. That's just how velocity addition works with super fast speeds.

With real materials it is different. Sound moves through air at 340 m/sec and in any frame other than that of the air, you add the frame speed to that (just like my superfast example above). So if you're moving at 500 m/sec, that's supersonic and it is impossible to hear anything behind you. That is a very frame dependent property, not just in name at all.

Thanks to all for your patience. I think I have it now

 

[vanhees71]

I think he's distinguishing his theory from both ether theory, where the speed of light is $c$ relative to the ether, and ballistic theory, where the speed of light is $c$ relative to the emitter.

I think Einstein wanted to give a physical operational definition of the reference frames involved, and indeed there are two frames of reference involved here: the rest frame of the light source and the observer's rest frame. Einstein's argument in the famous 1905 paper on moving bodies was in terms of a symmetry principle, i.e., in modern terms he demanded to find a spacetime description such that (a) the special principle of relativity is fulfilled (tacitly assuming also that in any inertial frame an observer finds the geometry of space to by Euclidean) and (b) the Maxwell equations are form invariant. So he had to find a spacetime description and transformation laws from one frame to the other for all the physical quantities involved in electrodynamics (em. field components, charge and current density, kinematics of "electrons").

The ingenious act was to precisely pick up the one most simple piece contained in the Maxwell equations, which is relevant to get the spacetime transformation and makes the Maxwell equations fail to be Galilei invariant: The appearance of a fundamental constant of the dimension velocity in Maxwell's equations, i.e., the phase velocity of electromagnetic waves, $c$, and the form invariance of Maxwell's equations implies that no matter how the transformation rules of all the em. quantities might look like, the space-time transformations must be such that the phase velocity of em. waves must be $c$ for any observer. Seen from the inertial rest frame of the light source this means that any observer moving with constant velocity in this frame observes the same phase velocity of the emitted light waves or, seen from the frame of any observer moving in the light-source frame the velocity of the light source.

This of course implicitly implied that there is no "aether", i.e., the em. waves are not oscillations of some elastic substance which would define another preferred frame of reference by its rest frame. Whether or not Einstein had the null result of the Michelson-Morley experiment in mind is not clear. According to his own recollection of events leading to his thoughts about the problem of electromagnetics in moving bodies, that was not the case.