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Period of a Wave

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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.

Wave Period Definition

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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.
Wave Period

Formula for Period of a Wave

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

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 $\lambda$
where, $\lambda$ is wavelength of a wave

Period of a Sine Wave

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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 $\phi$.

How to Find the Period of a Wave?

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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

 

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