Captain's Log: Supplemental
One more than one occasion, I have been asked by both people on the Enterprise and off if our Lt. Kurt is really a Vulcan who has been surgically modified to appear human. For years, at the request of the Vulcan High Council, I have done my best to deny any such claims.

But, with apologies to the Vulcan Ambassador, I must now come clean and reveal the truth, once and for all.

Lt. Kurt is really "Skurt", a Vulcan scientist placed on board the Enterprise to help us calculate the intricacies of currents, tides and Time-On-Time scoring.

We were doing so well at keeping it a secret, but Kurt's, I mean Skurt's, latest reply to Lt. Commander Mitch about the differences between AM and FM radio signals could not have possibly come from a human.

For documentation purposes, here is Skurt's reply:

Well, common sense says the peaks need to be hit to detect frequency changes unless you use special equipment that can measure the rate of the curve and interpolate based on the side band (which, as we talked about before is a relatively recent development). So the lower the frequency, the longer you need to wait to see the peaks, and so the longer it takes to detect a frequency shift (and therefore the lower the frequency of sound that can be produced).

A little back-of-the-envelope calculation says 20,000 Hz, what you would need for any reasonable FM signal, would need to be able to detect frequency shifts 40,000 times per second. So the lowest frequency signal that could be FM would be 40 kHz (note this is independent of how much bandwidth the FM signal actually spreads over).

40 kHz is 7500m waves which is pretty dang low frequency. Now there may be more technical reasons for not doing it, but they would have to be orders of magnitude larger than this to have an effect.

Aha, the problem is Carson's rule. The frequency range an FM band will occupy is calculated as 2*(D+V) where D is the difference between highest and lowest frequencies to be transmitted, and V is the peak deviation. This is a different limitation than the one I mention above which assumed you could narrow the band as much as possible and just talks about the frequency of the signal.

At 20 kHz for music (or 3 kHz for voice, but then why bother with stereo) That means the FM signal would have to vary a minimum of 80kHz in frequency. Thus the 40 kHz signal, minimum we discussed above, would have a maximum frequency of 120 kHz. The next valid FM band would have to start at 120 kHz and would go all the way to 200 kHz.

So while FM is technically possible in the lower frequencies, the spread would by so large you would only be able to fit 12 stations below 1 MHz, and wipe out all AM transmissions in that range. And of course this assumes all FM interference could be eliminated.


And, just in case there was any doubt, I have been authorized by Starfleet Command to release the following image from the bridge sensor logs. This is from Stardate 10562.4 when Kurt, I mean Skurt, was posted on the Enterprise prior to his surgery: