You might have noticed that I, quite unhesitatingly, use both terms –– time and frequency –– and it seems these two are intimately interrelated. In fact if you asked a physicist for a formal mathematical definition of frequency he or she would probably write down something very similar to

which just tells us that frequency, denoted by f is an inverse of a time period T. That is, just by taking an inverse of one of the quantities one can easily convert time into frequency and vice versa. As all physical quantities, time and frequency have their units of measure, which we are all probably familiar with –– we measure time in seconds and frequency in Hertz, where 1 Hertz is just an inverse of a second. I am sure it is not hard to imagine what a second is, but let me help you to better understand a Hertz. To gain some intuition about what it means, first think of an oscillating pendulum:

Imagine you took a stopwatch and counted that the cat’s body undergoes one oscillation cycle per second. It would be equally fair to say that the frequency of the cat’s oscillation is one Hertz, that is, one cycle per second. You can now see that the number of full oscillation cycles that the pendulum makes is precisely what we refer to as the frequency of the pendulum:

frequency = number of cycles per second

Why is this all so important? Well, you might have not realized it yet, but you can now quite naturally use the pendulum cat to measure time. How? You just determined with your stopwatch that it takes the cat one second to complete one round of oscillation. From this moment all it takes to know how much time elapsed since a certain event happened is to count the number of oscillation cycles the cat performed. This idea, quite obvious in the first approach, lies at the core of any modern clockwork mechanism you may have encountered. Regardless of whether you are wearing a mechanical or a digital watch on your wrist, inside it contains a certain type of an oscillator serving as a timekeeping element. It is this highly repeatable motion of an oscillator, that makes a modern clock extremely precise. At this point before going further let’s step back and recall how people learned to keep track of time with an ever increasing precision.

The Ancient Egyptians were the first to divide the day into two 12-hour periods and used large obelisks as a very simple sundial to track the movement of the sun. Later they invented water clocks that were stone vessels with sloping sides that allowed water to drip at a nearly constant rate from a small hole near the bottom. Twelve separate columns with consistently spaced markings on the inside were used measure the passage of “hours” as the water level reached them. As the time went on people kept coming up with better ideas how they could measure time more precisely. Things changed dramatically when a Dutch physicist and mathematician Christian Huygens demonstrated the first pendulum clock in 1656. As apparent from its name this type of a clock we all are familiar with uses an oscillating pendulum, a swinging weight, as its timekeeping element. The frequency of the pendulum is defined entirely by its length and its length only. The shorter the pendulum the faster it will oscillate. The faster it oscillates the more precise the clock based on such a pendulum will be as a higher frequency oscillator divides time into finer intervals.

A pendulum oscillating at a frequency of 10 Hz will have a period of oscillation equal to 0.1 seconds, the one oscillating at a frequency of 1 MHz (megahertz or one million hertz) will provide a precision of one microsecond

In other words our measurement will accumulate one second of uncertainty every million seconds or every eleven days.