Time and Cycles
The period ($T$) of a wave is the time it takes for one complete cycle of the wave to pass a given point. It is the mathematical inverse of frequency. While frequency tells you "how many per second", the period tells you "how many seconds per one".
Periods are used when timing is more intuitive than rate, such as the period of a pendulum, the orbital period of a planet, or the duration of an AC power cycle.
The Inverse Relationship
The relationship between period and frequency is absolute:
- As frequency increases, the period decreases.
- As frequency decreases, the period increases.
The Formula
Where:
T=
Period (seconds, s)f=
Frequency (Hertz, Hz)Example Calculation
The standard AC power in many countries has a frequency of $50 , \text{Hz}$.
- Invert the Frequency: $1 / 50 = 0.02 , \text{seconds}$.
Each cycle of electricity takes exactly $20 , \text{milliseconds}$.