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There is a question on a test which goes like this:

"Given two electromagnetic waves, one of wavelength 6.0 X 10-7 m and the other of wavelength 7.0 X 10-7 m, travelling in space. When the two waves meet in space, they combine (interfere) to form a wavelength of _______"

The answer is "none, they do not interfere."

My guess was that the wavelength would be the LCM of the two wavelengths, but it seems that I am wrong. Could someone explain this to me?

I doubt the question is trying to test knowledge of a distinction between photons interfering and their probabilistic wave functions interfering as we haven't learned that yet, although it is possible.

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    $\begingroup$ Welcome to the real world where you are being given borderline nonsensical test questions to which the person who made them up expects false answers to be given. $\endgroup$ – CuriousOne May 27 '15 at 20:51
  • $\begingroup$ possible duplicate of Does a photon interfere only with itself? $\endgroup$ – Gonenc May 27 '15 at 20:53
  • $\begingroup$ If I understand it correctly, I think that question explores a distinction between what is actually interfering the particles (photons) versus the probabilistic wave functions. I doubt this is the distinction which applies to the question as the (high school level) test didn't assume knowledge of quantum mechanics, although it is possible. Do you think I have a reasonable case to challenge the question? $\endgroup$ – John Rowley May 28 '15 at 0:08
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Since two wave aren't not coherent (i.e, different frequency), they cannot intefere with each other.

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  • $\begingroup$ What about the result of "beats" in the context of sound waves of different frequencies? Or does that not apply to electromagnetic waves because they are transverse instead of longitudinal? $\endgroup$ – John Rowley May 28 '15 at 20:29
  • $\begingroup$ In fact, interference is the mathematical sum of waves. For two waves of different frequencies, interference does occur in manner that the envelope of the summing wave has equal maxima (constructive) and minima (equal to 0, destructive), such as beat. For ideal case, two waves has the same frequency, and the envelope become two parallel lines. In high school as well as in general program of some universities, only the ideal case is considered. So, for cases differing from the ideal cases, interference cannot occur $\endgroup$ – Lê Dũng May 29 '15 at 2:35
  • $\begingroup$ I think I understand -- the question is really a matter of definitions. If you define interference as a change in the amplitude of a wave at a certain point, the scenario in question would constitute interference, but if you define interference as a result in an ideal case, it would not. Am I understanding this correctly? $\endgroup$ – John Rowley May 29 '15 at 2:58
  • $\begingroup$ Additionally, do you think that it would be incorrect to say that the wavelength of the result in the described scenario is the "Least Common Multiple" of the previous two wavelengths? $\endgroup$ – John Rowley May 29 '15 at 3:00
  • $\begingroup$ frequency of the resulting wave is the arithmetic mean of two initial frequencies. However, the frequency of the envelope is $f=|f_1-f_2|$. From this, you can derive the answer for wavelength. $\endgroup$ – Lê Dũng May 29 '15 at 3:10
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Say if at any instant resultant amplitude is zero or maxima at point of interference the next instant it will change as time variations of two waves is different. Means that there interference at a particular point is changing with time. At the time it is showing a maxima a wave packet will originate which is a comlex wave of ($\lambda_{1} + \lambda_{2}$) the next instant the whole scenario will change as may there may be no wave coming. So in such cases we do not say sustained interference. What we will observe is uniform intensity everywhere of complex wave.

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