It’s time for another quick lesson in the basics. Today I’d like to talk about frequency and how it is related to time. First of all, frequency is a rate; that is, how many “somethings” happen in a given period of time (units of “per (unit of time)”).

Take a watch with a second hand. The second hand “ticks” sixty times during every minute. Its rate of ticking is sixty ticks per minute. Since there are sixty seconds in one minute, that also means that the second hand ticks at a rate of one tick per second. The standard SI measurement of frequency is “per second,” and the official name for this unit is the Hertz [Hz]. The namesake, Heinrich Hertz, was a 19th century German physicist who made significant contributions to the field of electricity and magnetism (no pun intended ;)), and we honor him with this unit.

Since a rate describes something happening repeatedly, it can often be rightly assumed that the action in question is identical every time. When the identical action happens repeatedly, we call that a periodic action. Period is the inverse of frequency; that is, how many seconds happen between actions. For example, if you get paid two times per month, then the period of your paychecks is roughly two weeks. The whole course of action from when something occurs to when it occurs again is often called one cycle (by the way, ladies, these words aren’t coincidental!).

Consider a kid on a swing at the playground. Actually, swinging is one of my favorite things to do, so let’s consider me on a swingset! Once I seat myself and get going, I can keep myself swinging at a pretty steady rate. Since the seat is confined on a chain, I can define a certain path that I travel and cannot deviate from. I can also define a certain point on this path as a starting point; let’s call it the very bottom of my motion. The time it takes me to swing from the bottom, up to the front, back through the bottom, up to the back, and return to the bottom is one cycle of my motion. If it takes me two seconds to complete one swing cycle, my frequency is one swing per two seconds, or one-half cycle per second, or 0.5 Hz.

This is a very basic example of what we call an oscillator. An oscillator is anything that, well, oscillates! But physically speaking, we like to limit it to oscillators that are very regular in the length of the cycle. And what better example of an oscillator than, you guessed it, a clock! Like we mentioned at the very beginning, typical clocks and watches tick at a steady rate of 1 Hz. But the clock in your living room or on your wrist will eventually slow down as the battery dies, or as the pendulum swings down, or even as the components wear out. Some clocks are made from quartz, which is a material that has the peculiar quality of oscillating at a very steady frequency when an electrical current is applied. However, even its frequency will wander off a little due to the nature of the atoms inside. For you and me day-to-day, this isn’t a big deal. But, as I mentioned in my previous post about time, for ultra-precise measurements it can make a big difference.

So the name of the game in my field of work is developing clocks that tick at a frequency that does not vary, up to fifteen or sixteen decimal places…or more if we can! The current basis for these oscillators is the internal workings of sub-atomic particles, but that’s a story for a different day. The next step will be taking what we have learned about time and frequency and start making the connection to light and lasers…in bite-sized pieces of course! Thinking with your brain full is very impolite—and sometimes dangerous. We’ll take it slow, I promise. 🙂

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Appendix: Sine and Cosine Functions

*If you want a little more math, read on*! Oscillators can be modeled with the mathematical functions sine (sin) and cosine (cos). The position, *x*, of an object undergoing steady oscillation can be mapped out as a function of time, *t*, by the equation *x*(*t* ) = *A* sin(*ωt *), if we know the amplitude, *A*, (the maximum distance away from the center of motion) and the frequency, given by the Greek lower-case letter omega, *ω*. Here’s a very basic graphic for a refresher.