How are period and frequency inter-related?

Our definition of the period of something is simply how long it takes, and is measured in seconds. For a periodic waveform, we define its fundamental period (known simply as its period) as the time it takes to comple one cycle of vibration. Our definition of the frequency of something is simply how many times it occurs within some space of time (for example the frequency of a bus service is expressed in 'number of buses per hour').

For sound waves, the vibrations are often very rapid and we get a large number of vibrations occurring within one second. So we measure the fundamental frequency of a periodic sound in terms of how many cycles of vibration occur within one second, or in other words, units of 'per second' or s-1. However, this unit also has a special name in the S.I. system, called Hertz (Hz).

Given these two definitions, then, we can say the the fundamental frequency in Hertz of a periodic waveform is simply the number of fundamental periods it completes in one second, i.e.

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