How are frequency and period related in waves?

Answer 1

Mathematically, frequency = (1/Period)

Conceptually, the period is how long it takes a wave to begin repeating itself. For example, if I start a stopwatch when the wave reaches its peak, and then stop timing when it reaches its next peak, the time on the stopwatch is the period.

The frequency is how far the wave gets in 1 second.

Some examples:

If it take a wave 30 seconds to go through one cycle, the period is 30 seconds. In 1 second, it gets only 1/30 of the way through its cycle. Its frequency is 1/30 then.

If a wave repeats itself 10 times in 1 second, its frequency is 10. It's period must be 1/10 of a second.