This is a two part question and something I think I should know off the top of my head, but I don't, and I can't find a ready answer to it on at least a cursory search.(adsbygoogle = window.adsbygoogle || []).push({});

The first part has to do with defining a frequency of a wave in general. I can sit here and tap out a beat on a drum that executes 5 cycles (taps) in 2 seconds. Ostensibly, that appears to me to be a beat frequency of 2.5 cycles per second (cps), or Hertz. I can similarly imagine a water wave or electromagnetic wave beating out the same frequency. However, I've never heard of a fractional frequency as such. Do these exist? In my example of my tapping on a drum again, my "rough assessment" is that the frequency was 2.5 cps, but I'm probably off of that a little in each cycle, so the actual frequency of the oscillations are likely described by an irrational number. Yet again, I've never seen a fractional frequency described. Perhaps it has to do with only an integer number of cycles being able to fit on a unit circle? I don't know the answer to this, please help.

The second part of the the question relates the above to the Planck-Energy relationship, E=hf. I'm assuming that you find the energy of an electromagnetic (EM) wave by taking the integer value of it's frequency and then multiplying that by Planck's constant. Sounds fair enough. But why are we so confident that every EM wave has an exact integer value that we can use for the calculation?

I think a confusion, for me at least, arises here over the meaning of the concept of "quantization." My understanding of quantization is generally that it arises because standing wave patterns that describe particles must have integer values that fit into a 2π circumference. But then you also have Planck's constant that appears to quantize energy, momentum, etc. in terms of the numerical value "chunk" of that constant. Which of these two serves as the canonical "chunk" of quantization? Again, this relates back to the traveling wave example above. If the oscillation is not confined to some sort of potential well that constrains an integer value of it's frequency, then isn't there a relatively continuous distribution of non-integer frequencies possible for say, any given electromagnetic wave?

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# Frequency oscillations and Planck's constant

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