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I learn the property of standing wave in undergraduate project some times ago. From my text, two opposite propagating waves add up to a wave with node staying in place my amplitude is oscillating in time as

$$ \cos(kx + \omega t) + \cos(-kx + \omega t) = 2\cos(\omega t)\cos(kx) $$

I saw an experiment with using an string with one end is oscillating at finite frequency ($\omega/2\pi \sim 100 \ \text{Hz}$), it is clear to see the standing wave.

And I read a material about using two counter-propagating laser to create the standing wave in space. If that is implemented, will we really see the standing wave or not. It is confusing me because the frequency of laser is very high, the term for oscillating term $\cos(\omega t)$ is averaged to be zero at that high frequency. So how can we really create standing wave with laser as stated in some literature?

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Standing waves are routinely created in laser cavities. As far as I understand, they were demonstrated using "evaporated pattern on thin metallic film at small angle in laser cavity" (https://books.google.com/books?id=v1v0BwAAQBAJ&pg=PA19&lpg=PA19&dq=%22Experimental+Confirmation+of+Standing%22&source=bl&ots=MMZmJP0cVb&sig=ZvLDXbLHTEwyswPeXUe3wCYiX-c&hl=en&sa=X&ved=0ahUKEwj1lrz_-PbPAhVIWSYKHQCDAmoQ6AEITDAI#v=onepage&q=%22Experimental%20Confirmation%20of%20Standing%22&f=false ), but I don't have access to this article. If I had to speculate, I would think that a very thin metal film was placed into a Fabry-Perot interferometr at a small angle to the axis. The evaporation pattern on the film would depend on the average local intensity of the electric field. Due to the small angle, the period of this pattern could be significantly larger than the wavelength of the light.

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  • $\begingroup$ I am not sure that these are legitimately called standing waves youtu.be/RxzMzSZF_b4 $\endgroup$
    – user108787
    Oct 25, 2016 at 22:15
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    $\begingroup$ @CountTo10 : I don't understand why a standing wave (say, a single longitudinal mode) in a Fabry-Perot cavity cannot be called a standing wave. Neither do I understand how the youtube video is relevant to my answer (in the video, a laser beam is reflected on a vibrating membrane, if I understand correctly). Could you please explain? $\endgroup$
    – akhmeteli
    Oct 25, 2016 at 22:24
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    $\begingroup$ Sorry, I had never seen the phenomenon before and have no experience with experimental techniques , as I entirely self study. My sincere a pologies for the inconvenience and time-wasting. $\endgroup$
    – user108787
    Oct 25, 2016 at 22:40
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Not all standing waves are necessarily physically observable (or audible), and you are right with regards to laser light interference you would not be able to observe the standing wave, at least with your naked eye.

Optical flats rely on the principle of standing waves, and in this case you can see the outcome of light interfering as a visible pattern.

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  • $\begingroup$ Thanks for your reply. But in some articles I am reading, it is said that the optical standing wave is used in some case call optical lattice in cold atom. So in such high frequency so the average amplitude to be flatted out, is it really a standing wave or just a constant background for the particles? $\endgroup$
    – user1285419
    Oct 25, 2016 at 22:11
  • $\begingroup$ so then you are not really considering two separate laser sources "in space" (vacuum) but rather laser light propagating in a super cooled crystal lattice? $\endgroup$
    – docscience
    Oct 25, 2016 at 22:18
  • $\begingroup$ I am not familiar with that but from what I understand from some introduction article, that optical lattice is not a real crystal lattice, it is just a periodic structure formed by optical beams of the standing wave form. $\endgroup$
    – user1285419
    Oct 26, 2016 at 0:18

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