Explanation of Interference of Electromagnetic Waves

Question

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.

Answer 1

Since two wave aren't not coherent (i.e, different frequency), they cannot intefere with each other.

Answer 2

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.