This is an offshoot of the Crackpot Index thread. There are some misconceptions about a very simple concept in that thread: frequency.

This is probably somewhat esoteric, but I’m trying to be as plain as possible. If anyone has any questions or corrections let me know.

Frequency is the reciprocal of the period of a cyclical process.

The period is measured in seconds (the amount of time of time between one cyclical event and the next), and the frequency is one over the seconds, or s^-1, otherwise known as hertz (Hz). That’s where your computer’s ‘hertz’ rating comes from. I think our family’s first brand-new computer was 127 megahertz (it also had a 1.6 gigabyte hard drive ). Computers now operate in the realm of multiple gigahertz. My wife is the computer engineer, but the layman’s definition of this number is it tells you how many times a second your computer can turn its transistors on and off.

One of the cool things nobody really talks about in geometry class is how important the geometric functions of sine, cosine, tangent, and their inverses and reciprocals are. Yes, they’re great for finding the length of the unknown side or the unknown angle of a triangle, but that’s probably their least important application. Among their many other uses, sinusoidal functions are used to model periodic functions like waves and exponential decay. Here’s an example of some light waves:

The above waves all have about the same amplitude (vertical distance from the peak or trough is one way to measure it), but their wavelength changes (horizontal distance from peak to peak or trough to trough). The decreasing wavelengths increases the measured hertz (frequency), as can be seen in this gif:

And here’s an example of exponential decay of a spring-mass-damper system. The graph isn’t made for that animation, but it’s a good visual approximation of a graph of the vertical motion of the mass over time:

The point is all kinds of stuff can be modeled with sinusoidal functions which are ways of describing, among other things, the period and frequency of the thing to be modeled. Frequency is important and fun. Just don’t ask me to do a Fourier Transform.

All the above images came from Almighty Wikipedia.

Now for the not so good images. They’re rough and not to scale, but hey, I made them at great personal expense of time so back off.

Here’s the discussion on the misconception from the other thread. It’s about how an atomic clock works. There’s a theory out there that the speed of light is actually variable…okay, whatever. Let’s assume that’s true.

The misconception is that if there is a change in the speed of light then there is an effect on the length of the second because the length of time it takes to travel between the atoms emitting radiation and the sensor is longer. This is wrong.

I’ve created an imaginary atomic clock that ticks three times every second. Here are two identical clocks, one where the speed of light is slower than the other. Here they are starting at the same time:

At first glance, then, this seems to confirm the theory that the actual speed of the radiation changes the second. But watch what happens if we start them at different times:

You can see that the length of time between when the first signal enters the receiver and when the last enters the receiver is the exact same for both clocks. Here it is shown a different way. One receiver is put further away from the other:

So you see, the speed of the radiation doesn’t matter. Only the frequency at which the radiation is emitted matters in the definition of the second.

Now let’s change the frequency of the clocks themselves and leave the speed of the radiation constant:

You can see the varied frequency of the emission creates a time difference between the two clocks. This could be caused by a variable speed of light, but the relationship would be very complicated and it would look slightly different from this. It would be a combination of the first gif and the last gif.

So…any questions?