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# What is the relationship between frequency and period?

Frequency, f, is how many cycles of an oscillation occur per second and is measured in cycles per second or hertz (Hz). The period of a wave, T, is the amount of time it takes a wave to vibrate one full cycle. These two terms are inversely proportional to each other: f = 1/T and T = 1/f.

For example, if a wave takes 1 second to oscillate up and down, the period of the wave is 1 second. The frequency is the reciprocal of that, 1 cycle/sec, because only one cycle occurred in a second. If, however, a wave took half a second to oscillate up and down, the period of that wave would be 0.5 seconds, and the frequency would be the reciprocal, or 2 cycles per second. So, you see that a wave with a long period has a low frequency, while a wave with a short period has a high frequency.

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