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Frequency to Wavelength

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The notation of wave is something familiar to everyone in one form or another whether it be ocean waves, sound waves etc. In many cases an observed wave is the result of a disturbance moving through a medium such as water, air etc. As the disturbance is transferred from one part of the medium to another,we are able to observe the location of the disturbance as it moves with speed in a particular direction. The basic parameters like frequency and wavelength of a wave is related to each other. The relation between these two quantities are described in the following section.

Frequency is nothing but the number of waves passing though a particular point with a unit time. It is denoted by f and measured by a unit of Hz. Wavelength is given as the distance between consecutive crest or trough of a wave. The notation for wavelength is $\lambda$ and unit is meter. Frequency and wavelength are inversely proportional to each other. If the frequency is high, wavelength is small and vice versa.

Frequency and Wavelength
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Frequency from Wavelength Formula

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Frequency and wavelength can be related by velocity of light. These parameters are inversely proportional.
The conversion relation is,
$\lambda$ = $\frac{c}{f}$
where,
c is the velocity of light,
$\lambda$ is the wavelength,
f is the frequency of the wave.

Convert Frequency to Wavelength

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The given problems will help to understand the conversion between the above parameters.

Solved Examples

Question 1: Determine the wavelength of a wave if the frequency is 1050Hz?

Solution:
 
Given that,
Frequency, f = 1050Hz=1050s-1
Velocity of light, c = 3 $\times $ $10^8$m/s

The conversion equation is,
$\lambda$ = $\frac{c}{f}$
$\lambda$ = $\frac{3 \times 10^8}{1050}$ = 28.57 $\times $ $10^4$m

 

Question 2: Frequency of a wave is given as 500Hz, calculate the wavelength of that wave?

Solution:
 
Given that,
Frequency, f = 500Hz = 500s-1
Velocity of light, c = 3 $\times $ $10^{8}$m/s

The conversion equation is,
$\lambda$ = $\frac{c}{f}$
$\lambda$ = $\frac{3 \times 10^8}{500}$ = 6 $\times$ $10^5$m