Derive a relation between time period anf frequency of a wave

The relation between frequency and time period is given by:

f = 1/T

Explanation:

In a wave motion, the particle move about the mean position with the passage of time. The particles rise to reach the highest point which is crest, and similarly falls to reach the lowest point which is trough. The cycle keeps on repeating.

The time period of the wave can be defined as the time taken to complete one such cycle. Time period is given by:

T = 2π/ω

Frequency can be defined as the number of cycles completed in unit time, which can be taken as the inverse of time period. frequency is given by

f = ω/2π

or

f = 1/T