Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

Period, Frequency, and Amplitude

The figure shows our most basic example of a vibration. With no forces on it, the spring assumes its equilibrium length, (a). It can be stretched, (b), or compressed, (c). We attach the spring to a wall on the left and to a mass on the right. If we now hit the mass with a hammer, (d), it oscillates as shown in the series of snapshots, (d)-(m). If we assume that the mass slides back and forth without friction and that the motion is one-dimensional, then conservation of energy proves that the motion must be repetitive. When the block comes back to its initial position again, (g), its potential energy is the same again, so it must have the same kinetic energy again. The motion is in the opposite direction, however. Finally, at (j), it returns to its initial position with the same kinetic energy and the same direction of motion. The motion has gone through one complete cycle, and will now repeat forever in the absence of friction.

The usual physics terminology for motion that repeats itself over and over is periodic motion, and the time required for one repetition is called the period, T (the symbol P is not used because of the possible confusion with momentum). One complete repetition of the motion is called a cycle.

We are used to referring to short-period sound vibrations as "high" in pitch, and it sounds odd to have to say that high pitches have low periods. It is therefore more common to discuss the rapidity of a vibration in terms of the number of vibrations per second, a quantity called the frequency, f. Since the period is the number of seconds per cycle and the frequency is the number of cycles per second, they are reciprocals of each other,

f = 1/T .

 A carnival game.

 Period and frequency of a fly's wing-beats.

Units of inverse second, s-1, are awkward in speech, so an abbreviation has been created. One Hertz, named in honor of a pioneer of radio technology, is one cycle per second. In abbreviated form, 1 Hz=1 s-1. This is the familiar unit used for the frequencies on the radio dial.