A wave is a sort of disturbance that travels through a medium from a point to another transferring energy. Each wave has its own amplitude, wavelength, frequency, period, crest and troughs. The frequency tells with what speed a wave move, if it makes certain number of oscillations for a certain time interval. This period is nothing but the period of the wave. |

The wave period describes the same thing as it does with a pendulum. It is the time taken by a wave to complete one cycle. It's known that wave has a crust and trough. So how many times a crust or a trough passes a given point is its wave period.

The period of a wave is expressed as the reciprocal of the frequency given asT = $\frac{1}{f}$

Frequency is the number of troughs or crests that passes a given point per unit time, and period is the time between the passage of two successive troughs or crests.

The velocity of a wave V is given as,

V = $\frac{\lambda}{T}$

or

V = f $\lambda$

or

V = f $\lambda$

where, $\lambda$ is wavelength of a wave

The period of sine wave is of the form **y = A sin ($\omega$ t + $\phi$)**

Here,

A is the amplitude of the sine wave,

$\omega$ is the angular frequency,

t is the time in seconds and

the phase shift is $\phi$.

A is the amplitude of the sine wave,

$\omega$ is the angular frequency,

t is the time in seconds and

the phase shift is $\phi$.

**Lets go through some examples on period of a wave:**

### Solved Examples

**Question 1:**Calculate the period of the wave that has frequency of 20 Hz.

**Solution:**

Given:

Frequency f = 20 Hz

The period of a wave is given as,

T = $\frac{1}{f}$

= $\frac{1}{20}$

= 0.05 s

= 50 ms

= $\frac{1}{20}$

= 0.05 s

= 50 ms

**Question 2:**Calculate the frequency of the wave if it completes the oscillation in 60 ms.

**Solution:**

Given:

Time period T = 60 ms

The frequency of a wave is given as,

f = $\frac{1}{T}$

= $\frac{1}{60 \times 10^{-3}}$

= 16.7 Hz

= $\frac{1}{60 \times 10^{-3}}$

= 16.7 Hz