If I have a source of photons where photons have $f$ frequency and the emitting frequency of the source is $f'$, what is the frequency of the resulting EM wave?
Essentially, we have a source that emits photons that each have a frequency of f, but the frequency of their production by the source is f′.
Answer
If I understand you correctly, you're saying that you have a source that emits photons that each have a frequency of $f$, but the frequency of their production by the source is $f'$.
Well, then the frequency of the emitted waves is the same as the frequency of the photons, i.e. $f$. The rate of their emission doesn't matter.
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