Period and Frequency

In a periodic ac wave, the kind that is discussed in these topics (and throughout the rest of this book), the function of instantaneous amplitude versus time repeats itself over and over, so that the same pattern recurs indefinitely. The length of time between one repetition of the pattern, or one cycle, and the next is called the period of the wave. This is illustrated in following Figure for a simple ac wave. The period of a wave can, in theory, be anywhere from a minuscule fraction of a second to many centuries. Period, when measured in seconds, is denoted by T.

Untitled
A sine wave. The period is the length of time it takes for one cycle to be completed.

Originally, ac frequency was specified in cycles per second (cps). High frequencies were sometimes given in kilocycles, megacycles, or gigacycles, representing thousands, millions, or billions (thousand-millions) of cycles per second. But nowadays, the unit is known as the hertz (Hz). Thus, 1 Hz = 1 cps, 10 Hz = 10 cps, and so on. Higher frequencies are given in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz). The relationships are as follows:

1 kHz = 1000 Hz
1 MHz = 1000 kHz = 1,000,000 Hz = 106 Hz
1 GHz = 1000 MHz = 1,000,000,000 Hz = 109 Hz
Sometimes an even bigger unit, the terahertz (THz), is used to specify ac frequency. This is a trillion (1,000,000,000,000, or 1012) hertz. Electrical currents generally do not attain such frequencies, although some forms of electromagnetic radiation do.

The frequency of an ac wave, denoted f, in hertz is the reciprocal of the period in seconds. Mathematically, these two equations express the relationship:

f = 1/T and T = 1/f

Some ac waves have only one frequency. These waves are called pure. But often, there are components at multiples of the main, or fundamental, frequency. There can also be components at odd frequencies. Some ac waves have hundreds, thousands, or even infinitely many different component
frequencies.