Re: Beats: quiz question

["John S. Denker" <jsd@MONMOUTH.COM>]

SSHS KPHOX wrote:

> Today I put this question on a Waves test.

> 4. In color theory red light (4.8 x 1014 HZ) and green light (5.7 x
> 1014 Hz) combine to yield yellow. A student proposed that this is an
> example of the beats phenomenon.
> a. What would be the beat frequency
> of these colors? Would this be an observable frequency?
> b. Is the student justified in his hypothesis?

<digression>
  OK, I suppose we are taking for granted that
  everybody knows that yellow, red, and green
  pure spectral colors exist.  Roy G. Biv and
  cyan and chartreuse and various other things
  if you look closely and have enough vocabulary.
</digression>

The numerical answer to the Gedankenexperiment
(part a) is quite sufficient to disprove the
hypothesis (part b).

> The average of these two frequencies is in the yellow. The difference
> is IR, I think.

Sans doute.

> I just wanted to do something that was not sound.

Not sound?  That's quite a double-entendre.
 -- unsound reasoning?
 -- or just non-acoustic?  :-)

> One student said that beats only happens with sound. I know better
> than that.

If we are feeling generous, we could credit the
student with half-expressing a true fact:  a
0.1% frequency difference between two acoustic
tones has a timescale human neurons can deal
with, while a 0.1% frequency difference between
two optical lines does not.  So the latter
will not be perceivable without some serious
instrumentation.

But on the other side of the same coin, waves
are waves, and almost anything that happens
with sound has an analogy in optics.

As a fairly familiar example, your typical green
lasers (including the whizzy green laser pointers)
are made by frequency-doubling an IR laser.

The present-day telecom industry pretty much depends
on optical fibers, and you aren't going to make a
transmitter or a receiver without nonlinear optical
elements.

There are some very heavy books on nonlinear optics.
The topic gets pretty complicated pretty fast.

========================

There remains a moose on the table.  Everybody has
been avoiding the obvious question:  What's the
basic physics here?  What are the necessary and/or
sufficient conditions for beats to be perceivable?

This is a hard question.  This is definitely not a
high-school question.  It's not even an undergrad
question.  It might be amusing to spring it on
some know-it-all grad student during an oral
admission-to-candidacy exam or some such, and watch
'em squirm for an hour or two.