Period and Frequency

Any motion that repeats itself at regular intervals of time is called periodic motion. The smallest interval of time after which the motion is repeated is called its period.

Ø Let us denote the period by the symbol T.

Ø Its SI unit is second.

For periodic motions, which are either too fast or too slow on the scale of seconds, other convenient units of time are used. The period of vibrations of a quartz crystal is expressed in units of microseconds (10^–6 s) abbreviated as µs. On the other hand, the orbital period of the planet Mercury is 88 earth days. The Halley’s comet appears after every 76 years.

The reciprocal of T gives the number of repetitions that occur per unit time. This quantity is called the frequency of the periodic motion. It is represented by the symbol ν. The relation between ν and T is

ν = 1/T ------ (1)

The unit of ν is thus s^–1. After the discoverer of radio waves, Heinrich Rudolph Hertz (1857–1894), a special name has been given to the unit of frequency.

Ø It is called hertz (abbreviated as Hz).

Thus,

Ø 1 hertz = 1 Hz =1 oscillation per second =1s^–1