# Speed of light vs speed of sound

1. Apr 15, 2015

### doaaron

Hi all,

I originally posted this question as a reply to another post, but afterwards I thought it would be better to start a new thread. Unfortunately, I couldn't figure out how to delete the old post. With that out of the way...

In the experiment, we send either light or sound from a source, and calculate the speed of the wave as (d1 + d0)/(t1 - t0). My understanding is that for light, the calculated speed will be c regardless of v. However, for sound travelling in a stationary medium such as air, its speed in a stationary frame of reference will be independent of v, but the speed calculated by the receiver, (d1 + d0)/(t1 - t0) depends on v.

Am I going wrong somewhere? Earlier, one of the other members mentioned that the speed of sound is independent of the speed of the receiver, just like light.

thanks,
Aaron

2. Apr 15, 2015

### PWiz

That's right - the speed of sound is simply dependent on the temperature and density of the medium. Once a wave is set up, the speed of propagation of the wave will be independent of the relative velocity of the source.

3. Apr 15, 2015

### wabbit

The speed of propagation of the wave relative to the observer is affected by the observer speed by addition of velocities. However, the relativistic addition formula says that :
$$\forall v, c\oplus v =c$$
$$v_1\ll c, v_2 \ll c \Rightarrow v_1\oplus v_2\simeq v_1+v_2$$
So you get the two different results for light and soundwaves.

4. Apr 15, 2015

### doaaron

Hi all,

thanks for the replies.

Sorry I didn't make my question clear. I understand that the speed of sound is independent of the speed of the source. In my example, the source and the receiver are the same, however, I am more interested to know if the speed of sound is dependent on the speed of the receiver. In my example, the speed of sound as measured by the moving receiver seems to be clearly affected by the speed of the receiver. The same isn't true for light.

This is what I had understood, but according to another member, (post #6 at the following link)

So I would like to confirm that the above statement is incorrect with emphasis on the speed of the receiver. Assuming it is incorrect, my next question is, have there been any experiments to test the speed of light with a moving receiver rather than a moving source?

thanks,
Aaron

5. Apr 15, 2015

### wabbit

I think I agree with that other poster, but actually I am not sure we can make general statements (speed relative to what ? Is there a medium of progagation ? )

I would say that
- the speed of the wave relative to its medium of propagation is constant. This brings an issue for light in vacuum, but it's ok since c is invariant anayway, so light propagates at c wrt the vacuum, whatever velocity we may arbitrarily assign to that vacuum.
- the emitter movement wrt the medium has no impact on that (it does yield a shift in frequency but this is another matter - let's assume for simplicity that the wave velocity is independent of frequency here), but the wave speed relative to the emitter is impacted and can be calculated by addition. Typically, we don't care about it (except for instance for supersonic emitters travelling faster than the wave the emit).
- the receiver has no impact either (though his perceived frequency is affected), except that we may care to inquire about the wave velocity relative to him, which is again obtained by addition.

I think the simplest way to view it is in the medium rest frame, then transform to whatever frame we are interested in.

In the case of light in a vacuum, c survives any addition unharmed, so the result relative to any observer is always c. But in case of light in a physical medium, slowed down to significantly below c, I can't see why the same formulas as for sound waves wouldn't apply.

Last edited: Apr 15, 2015
6. Apr 15, 2015

### Staff: Mentor

I would agree that the different unstated assumptions about frame of reference make what look like identical statements actually not.

The speed of light is fixed in the observer's frame, but the speed of sound is fixed in the medium's frame.

7. Apr 15, 2015

### doaaron

Hi russ_watters,

I intended for the receiver to be the frame of reference since it is the one which takes the measurement. Perhaps this was misunderstood by harrylin in my previous thread. Anyway you also seem to agree with my intuition, so I am still curious if it has been experimentally proven that the speed of a receiver has no influence on the measured speed of light.

Hi wabbit,

For simplicity we can just assume the medium is dead air for the sound setup, and a vacuum for the light setup.

This is kind of a viewpoint I hadn't considered. My assumption was that either sound and light are different (i.e. light speed is independent of receiver but sound speed is dependent), or they are the same, and both light speed and sound speed are independent of the receiver. As far as I understand it, and correct me if I'm wrong, there is no evidence that the speed of light is dependent on the speed of the receiver, regardless of the medium.

Facts.........................................................Light..........Sound.........Experiment
===============================================================
Speed dependent on source?....................No...............No.............De Sitter
Speed dependent on medium?.................Yes..............Yes..............Fizeau
Propagates in vacuum?.............................Yes...............No.............Obvious

* Michelson Morley? This experiement as I understood was used to detect the presence of an ether. Does it also show that light is unaffected by the speed of the receiver?
** My understanding.

thanks,
Aaron

8. Apr 15, 2015

### wabbit

The speed of light relative to that receiver ? I'd be surprised. Say light is slowed down to 1cm per second in some kind of medium in a 2m long tube, you send a pulse from one end then run to the other end and look into the cube. Do you think you can't overtake the light and see the pulse from the other end ? And you could do that without stopping, just having at a constant speed wrt the tube (and hence that same speed minus 1cm/s wrt the light). A wave is a wave is a wave : )

But I admit I don't know of experiments demonstrating that.

Last edited: Apr 15, 2015
9. Apr 15, 2015

### doaaron

Hi wabbit,

I meant that for a given medium, the speed of light is constant. i.e. Once you chose a medium, the speed of light within that medium is independent of the speed of the receiver. You thought experiment only proves that the speed of light is dependent on the medium which is understood.

that's exactly what I'm trying to figure :P

regards,
Aaron

10. Apr 15, 2015

### wabbit

Ah yes the speed of a wave in a medium, relative to that medium, is constant and doesn't depend on emitter or receiver. That was my point in post 5. This is true of sound as well as light.

But the speed of the wave relative to the receiver is the (relativistic) addition of the speed of the wave in (relative to) that medium, and the speed of the medium relative to the receiver (or minus the receiver speed relative to the medium). And this is also true for both light and sound.

I have no proof of this, but I find it hard to imagine how it could not hold. You could imagine a test particle travelling alongside that wave at the same speed in the medium : then this is just the composition of velocities for material objects. (and by the way the speed of the wave relative to that particle is zero, even if that wave is slowed down light.)

Actually you have something close to that with dispersion : if you send a pulse of red light and one of of blue light in a dispersive medium, they will travel at different speeds and one will overtake the other.

Last edited: Apr 15, 2015
11. Apr 15, 2015

### Staff: Mentor

These measurements have been done many times, to extremely high accuracy. This link is a good place to start. The summary is:

In a vacuum, the speed of the receiver has no measurable effect on the speed of light as measured by the receiver. (If the receiver is moving relative to the source, there will be a redshift or a blueshift from the relativistic doppler effect, but the speed is the same).

In a non-vacuum medium, the speed of light relative to the medium will depend on the characteristics of the medium. If the receiver is moving relative to the medium, then the speed measured by the receiver will be increased or decreased by the receiver's motion relative to the medium according to the rule for relativistic velocity addition.

Try this one. It's worth noting that the experiment was done in 1851, a decade before Maxwell's electromagnetic theory explained the wave nature of light and more than a half-century before Einstein discovered relativistic velocity addition.

12. Apr 15, 2015

### wabbit

Thanks ! So now I have proof : )

Just one comment, I prefer to think of the situation in a vacuum as no different than in a medium, and the same formulas apply - as they should, a vacuum being indistinguishable from an ether.

But the result is the same either way, a matter of taste I suppose.

13. Apr 15, 2015

### doaaron

Hi all,

OK. I guess I understand. For sound, however, since it travels nowhere near the speed of light, the speed of the receiver relative to the medium has a direct effect on the measured speed of sound. The light experiment in a vacuum is unique in that the wave cannot travel any faster...

I am trying to think along these lines too, but I cannot reconcile sound with light. From the above discussion, my intuition is that if light and sound were similar then the relativistic addition of velocities for sound would not depend on the speed of light. i.e. if you assume that a vacuum is kind of a perfect medium for light to travel and the relativistic addition of velocities has a result which is asymptotic to c, then what is the analogy with sound? Does sound have its own "perfect medium" with its own maximum speed?

regards,
Aaron

14. Apr 15, 2015

### PeroK

You're missing the fundamental point that in a vacuum, there is no difference between a moving source and a moving receiver. All motion is relative. So, a source moving away from a receiver is indistinguishable from a receiver moving away from a source.

The relativity of motion in a vacuum (and the absence of absolute motion) is essentially equivalent to the absence of an ether. If there were an ether, then light would propagate at a constant speed relative to the ether and observers would measure different light speeds depending on their speed relative to the ether. This is the Michelson-Morley experiment. No difference in speeds could be detected, so there cannot be an ether.

You could then ask: if there is no absolute reference frame in which light travels at "the speed of light in a vacuum", then in which reference frame does light travel at this speed? Well, the next simplest answer is "in all inertial reference frames". And, if you make that assumption, then you lose absolute space and time measurements and gain the theory of Special Relativity.

15. Apr 15, 2015

### doaaron

Hi PeroK,

the whole point of this thread is to understand the difference in propagation between light and sound (for me anyway).

Assume I am an observer in the rest frame and I measure the speed of light from a moving source. I would record the value as 3e8 m/s assuming the medium is a vacuum. Now do the same experiment with sound. Assuming the medium is air, the speed of sound would be 300 m/s. It is likewise unaffected by the speed of the source.

The same is not true if I were to consider a moving receiver and a stationary source in a vacuum for light, and air for sound. In the case of light, the speed would be unaffected by the speed of the receiver, but for sound, the measured speed would be almost a direct addition of velocities of the receiver and the sound. In fact, if the sound receiver were travelling at 300 m/s in the same direction as the sound itself, then the sound wave would never reach the receiver, and the receiver would conclude that the speed of sound is 0.

regards,
Aaron

16. Apr 15, 2015

### Staff: Mentor

Has it been clarified where those times and distances are measured? For sound it does not matter (for relevant velocities), for light it is important as different reference frames will get different measurements for times and distances.
If you measure them in the system of the mirror, then the speed is independent of the motion of receiver and emitter.

17. Apr 15, 2015

### doaaron

I thought that for light, the speed would be independent of the reference frame...I didn't bother with the actual measurements of time and distance for the light case, as it would over complicate things.

regards,
Aaron

18. Apr 15, 2015

### PeroK

That's because sound travels through an observable medium. So, all observers can measure their absolute speed relative to that medium.

If there were an ether, light would be the same.

It's the absence of an ether that makes light in a vacuum "different".

In a way, you seem to understand this difference fully. If sound could travel through empty space at other than the speed of light, there would be a problem. But it can't, so there isn't!

19. Apr 15, 2015

### Staff: Mentor

The addition of velocity for everything (including light, whether in a medium or not) depends on the speed of light in a vacuum, so including sound in there with everything else maybe isn't all that strange.

However, your intuition is also being led astray by a historical accident. What's really going on is that it is only mathematically possible to have zero or one constant-for-all-inertial-observers speeds (you can see this by trying to derive a transform analogous to the Lorentz transform under the assumption that there are two such speeds - you will find a contradiction). Experiments show that our universe operates according to the one-such-speed rules, so that's the velocity addition formula that we use. The historical accident comes in because at the time that relativity was formulated, light in a vacuum was the only thing known that moved at the invariant speed of our universe, so we naturally decided to call the invariant speed "the speed of light". This leads us to wonder why "the speed of light" appears in the velocity addition rule even for things that have nothing to do with light.... If we thought of the quantity c as a parameter of the universe from which many things, including the behavior of light, can be derived then its appearance in situations that have no obvious connection to light might bother your intuition less.

Last edited: Apr 15, 2015
20. Apr 15, 2015

### PeroK

You're forgetting that the behaviour of light in a vacuum is a manifestation of the absence of absolute space and time for all observers. So, it's not the speed of light, per se, that affects measurements of sound and velocity additions, but the relativity of space and time.