# Can you simulate a Michelson-Morley experiment with sound?

Is it possible to make a MME with sound waves? Suppose we travel on a rail platform with two "mirrors" that reflect sound, what parameters would we need to simulate the light experiment? would it work if we went at a proportional speed, that is 300/1000 m/s? How far should the mirrors be,... etc?

Can you figure out what the result of such experiment would be? Is the speed of propagation of sound influenced by motion throught the air?

Edit

In the interesting link provided by Farcher they say:

The results confirm the hypothesis that the two-way velocity of sound is isotropic in a moving system, as in the case of the optical MME

Does this mean that speed of propagation od sound is not affected by motion? Does this prove the relativity does not apply only to light?

• The problem with audible sound waves is that their wavelength is rather long but is can be done with ultrasound and here is an example worldnpa.org/abstracts/abstracts_5338.pdf Commented Feb 24, 2016 at 15:35
• To me it's not even clear why they are calling that experiment a Michelson-Morley. Half the setup is missing and there is no interference part. Since air also can't flow trough the mirrors (while space and the aether can!), one can never even compare the two cases. Commented Feb 24, 2016 at 20:56

I don't think it's practically possible. Here are some of the "why":

• It is a problem to create focused sound ray. Just cause of typical wavelengths and needed impedance parameters.
• To make it at significantly greater speed than ca. 350 m/s you would need to conduct the experiment in a liquid or (and that would be funny) in a solid substance.
• It would be really tricky to make a "half transparent" obstacle.
• In classical linear theory the speed of sound in a perfect gas is constant dependent only on ambient temperature and very weakly on humidity - not on the pressure disturbances. However, in nonlinear theory, which you probably would need to use to track very tiny differences, there is a dependence. ...and then the math suddenly became really ugly. The "nonlinear speed of sound" is for a planar progressive wave in a diatomic perfect gas usually given by:

$$c = c_0 + 0.02u$$

where $c_0$ is the "linear sound speed" and $u$ is acoustic particle velocity. And the there is a "semilinear" approach for convective speed in which the Mach number is a rate of dissimilarity to the steady case.

Just do the discussion based on characteristic $\lambda$ to get closer to "How far should the mirrors... etc.".

There might be some effects of nonlinear wave steepening due to the motion, but it would require very good anechoic room, very silent servo drives and really punctual signal processing work.

• I do not think it is totally out of the question. If you use an ultrasonic transmitter and receiver with exponential horns there is no need to focus. It might be fun doing the experiment travelling on the back of a lorry? A piece of hardboard is a very good half silvered mirror and sheets of aluminium are good reflectors. Commented Feb 24, 2016 at 15:47
• I agree, that is doable. The question is whether you want just to "see something" or qualitatively evaluate the MME. I am not sure about the latter case. Commented Feb 24, 2016 at 16:08
• There is a standard interferometer set up in schools with ultrasonic TX & RX. The wavelength of the ultrasonic waves is measured by moving one of the aluminium mirrors and looking for maxima and minima on a meter which is monitoring the output of the RX. What one would need to do is to mount the apparatus on a platform which could be rotated. Then the whole arrangement needs to be put on something which can move at a relatively constant speed, a lorry or a boat. Whilst moving the apparatus would be rotated and the output meter monitored. The path lengths are about 100 cm. Commented Feb 24, 2016 at 16:18
• Well, I think you should put this as an answer as well. I would certainly vote it up. Commented Feb 24, 2016 at 16:54
• Did you have a look at the reference I mentioned in a comment after your question? Commented Feb 24, 2016 at 17:12

I think it should be possible. Essentially you could construct a large L-shaped frame (each side being the same length) with two small flat surfaces at the ends of the L, and a source of a short sound -- a cap gun for instance -- and a microphone at the corner. Then you fire the gun and listen for the echoes, timing their arrival. How big the apparatus needs to be depends on how short your impulses are and how accurately you can measure: arms 10m long should be fine.

Now you put the whole thing on wheels, and find a very large flat surface (salt flat?) and, on a flat calm day, you drive it along in various directions, and do the experiment repeatedly.

There will be two problems to overcome:

1. there will be reflections from the ground, wheels and so on, but if you dimension things properly you can arrange life so that these arrive at times comfortably different (earlier) from the ones you care about;
2. there will be some dragging of the air by the structure itself, which is unavoidable but which you can work to minimise by making it have as small an effective cross-section as possible and by streamlining suitable bits of it (you may need to do wind-tunnel tests).

What you will find is two things (remember this is all being done on a flat calm day):

• by rotating the device and repeating the experiment at lots of angles but while stationary you will find that sound travels at a speed which is not direction-dependent, or that its speed is isotropic;
• by moving the device along with it turned at various angles to the direction of motion you will find that sound moves at a speed which is constant relative to the air, not the device, or in other words that there is 'aether' for sound, and it is, in this case, air.

What you will not get is a null result, as the Michelson-Morley experiment.

• I may not have been clear, but sound is affected by directional motion, in exactly the way you would expect. It's speed is the same in any direction (when the apparatus is stationary relative to the air), but that's a different thing.
– user107153
Commented Feb 25, 2016 at 11:02
• Propagation speed is the same in every direction relative to the air, not relative to you. There is no Doppler effect (there is only a Doppler effect when the source and detector are moving relative to each other, which they are not here).
– user107153
Commented Feb 25, 2016 at 11:58
• It's not null for sound! That's why it was a big deal when it was null for light. If I have done my sums right (not guaranteed before I have had coffee) then, if the frame is moving with one arm in the direction of movement and one perpendicular, the time for sound to travel the parallel arm and back is $t_\parallel = 2LV/(V^2-v^2)$, and for the perpendicular arm it is $t_\perp = 2L/\sqrt{V^2-v^2}$, where $L$ is arm length, $V$ is speed of sound in air and $v$ is how fast the frame is moving. And you can see that $t_\parallel < t_\perp$.
– user107153
Commented Feb 25, 2016 at 12:10
• I think $t_\parallel - t_\perp = Lv^2/V^3 + O(v^4)$.
– user107153
Commented Feb 25, 2016 at 12:23