Frequency and Period

Frequency tells you how many complete cycles of a wave happen each second, while period tells you how long one complete cycle takes. Since these two quantities describe the same motion from opposite viewpoints, they must be reciprocals: if one cycle takes a long time, fewer cycles fit into a second, and if one cycle takes a short time, more cycles fit into a second. That is why f = 1/T, with frequency measured in hertz (cycles per second) and period measured in seconds.

Use this formula whenever you know the time for one vibration, rotation, or wave cycle and want the number of cycles per second, or vice versa. It is common in sound waves, musical notes, pendulums, rotating machinery, and any periodic motion.

• Using the wrong units: period must be in seconds before finding frequency in hertz
• Multiplying by the period instead of taking the reciprocal
• Forgetting that frequency and period are inverse, so a bigger period means a smaller frequency