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Wavelength to Frequency

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Waves are created by a disturbance or a vibration. In the case of a vibrating string, the disturbance is the person shaking the end of the spring. If the disturbance is regular, as the waves travel along the spring ones can see a repeated pattern. The distance between a point and the next point along the spring where the pattern repeats is called the wavelength. The number of complete waves produced each second is called the frequency, f.  Wavelength and frequency are fundamental characters of any waves. These two parameters are inter related also.  

Wavelength to Frequency Equation

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As mentioned before, wavelength and frequency are related by a constant which velocity of light. If the wavelength is high for a wave, its frequency is low. So these quantities are inversely proportional to each other. The relation between them is given below:
f = $\frac{c}{\lambda}$
where,
c is the velocity of light,
$\lambda$ is the wavelength.

Energy of a Photon

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Photon is a packet or quanta of light energy. It is considered as an elementary particle.
Energy of photon is given by the equation,
E = $\frac{hc}{\lambda}$

where,
h is the Planck's constant,
c is the light velocity,
$\lambda$ is the wavelength of light.

Wave Number

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Wave number is defined as the number of waves per unit distance. In other words, wave number is given by the reciprocal of wavelength. It is denoted as $\bar{\nu }$. Wavelength is measured in meter or cent meter, so wave number is measured in m-1 or cm-1.

Wave number, $\bar{\nu }$ = $\frac{1}{\lambda }$

Convert Wavelength to Frequency

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Solved problems of wavelength to frequency conversion is given below:

Solved Examples

Question 1: Determine the frequency of a wave whose wavelength is 5416 $\times $ $10^{-10}$m?

Solution:
 
The given parameter is,
Wavelength, $\lambda$ = 5416 $\times $ $10^{-10}$m
We know that light velocity, c = 3 $\times $ $10^{8}$m/s

The conversion equation from wavelength to frequency is
f = $\frac{c}{\lambda}$
f = $\frac{3 \times 10^8}{5416 \times 10^{-10}}$
f = 55.39 $\times $ $10^{13}$s-1= 55.39 $\times $ $10^{13}$ Hz
 

Question 2: Calculate the frequency, if the wavelength is given as 478 $\times $ $10^{-6}$m?
Solution:
 
The given parameter is,
Wavelength, $\lambda$ = 478 $\times $ $10^{-6}$ m
We know that light velocity, c = 3 $\times $ $10^{8}$m/s

The conversion equation from wavelength to frequency is
f = $\frac{c}{\lambda}$
f = $\frac{3 \times 10^8}{478 \times 10^{-6}}$
f = 62.76 $\times $ $10^{10}$ s-1= 62.76 $\times $ $10^{10}$ Hz.