Frequency is a concept of events happening at even intervals over time. A typical frequency concept is miles per hour. If a vehicle is traveling at 60 miles per hour, every hour it will travel 60 miles (according to Captain Obvious). Now let's look at an analog clock. The second hand of a clock moves in a circle 60 times an hour. Every minute it sweeps a full 360-degree circle. In 15 seconds (a quarter minute) it moves 90 degrees. In 30 seconds (a half minute) it moves 180 degrees, etc.

If we analyze the clock in the time domain, we watch how the second hand moves as time goes by. The second hand makes a full circle every minute. That's 60 circles per hour. Now we have a frequency for the second hand. Let's call it 60 cycles per hour. Knowing the frequency, we can predict where the second hand will be at any particular time. For example, let's say that at a particular time we observe that the second hand is pointing straight up. Where will it be in three minutes and 45 seconds? That's three complete cycles plus 3/4 of a cycle. After each complete cycle the hand points straight up so we just have to see where the hand points after 3/4 of a cycle. That would be pointing horizontally to the left at the number nine.

Now, let's illustrate that on a graph. When we illustrate the time domain, time usually is represented as a line that goes from left to right. Moving from left to right along that line represents passing time. To make a graphical representation of a clock's second hand in the time domain, we could represent time along the horizontal axis and angle along the vertical axis. Such a plot would show a constant change in angle over time, which would be a diagonal line. If we reset the angle to zero with each cycle, we will get a "sawtooth" shape.

Now, let's see what happens if we increase the frequency. It now takes less time to complete a cycle. More cycles fit the graph, so the cycles get closer together. For example, a graph of the second hand compared to the minute hand of a clock would show that the minute hand takes much longer to complete a cycle than the second hand, creating a stretched-out sawtooth shape.

In the above graph, the second hand has cycled 10 times and the minute hand has moved only 60 degrees. To see a complete cycle of the minute hand we have to compress the graph enough to show at least 60 cycles of the second hand, as shown below.

This graph of the positions of the clocks hands over time presents a waveform. This is not a wave in the sense of an ocean wave. That's a different kind of wave. This is merely a graphical representation a quantity that changes repeatedly over time. Alternating current repeatedly changes over time so it can also be represented by a graphical waveform. The shape of an AC waveform depends on how the voltage or current changes over time.

As you will see in AC Waveforms, we use time domain graphs to illustrate how the voltage of alternating current changes over time. An oscilloscope (discussed in detail later) is an instrument that draws time domain graphs of voltage in real time.