Can light waves cause beats?

It's a rather late answer, but the paper Visible optical beats at the hertz level has just appeared on the Arxiv and this describes exactly the phenomenon you ask about. This image from the paper shows the experimental setup:

The light frequency is modified using acousto-optic modulators (labelled AOM in the diagram), and to make it look pretty a lens is used to produce interference rings and a beam splitter is used to produce two images (labelled A and B) that are inverses of each other. That is, A is dark when B is bright and vice versa.

The paper reports that the brightness variation can be easily seen with the naked eye up to about a frequency difference of 20Hz, beyond which persistence of vision makes the beating disappear.

Later: a reviewer has pointed out this video on YouTube that shows a very similar experiment.

The math of beats is absolutely the same for light as it is for sound, but ...

• Most light around us in incoherent, so does not form beats on macroscopic time or distance scales.

• It is hard to select to sources that could conceivable give visible beats Look at it this way the frequency of green light is around $ c /(500\text{ nm}) \approx 6 \times 10^{15} \text{ Hz} $. All the colors have frequencies of the same order of magnitude, so the beat frequencies of two randomly selected colors tend to be around $10^{13}$--$10^{14} \text{ Hz}$: much faster than your eye can detect. To construct a pair of sources that you could see beat would require controlling their frequencies to about 1 part in $10^{14}$. That's not easy.

A laser gyroscope detects 'beats' of light.

In a laser gyro, laser light goes in two directions 'round a ring, clockwise and counterclockwise. If the gyro is rotating, one laser direction will be at a slightly different frequency than the other, and their interference will create a 'beat'.