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Frequency and Wavelength

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Frequency is that what decides how many wave cycles pass by a point in a second whereas wavelength is the distance between two consecutive crust or trough.
Frequency-Wavelength
The speed of sound, light has their own value that is constant. Its only the frequency and wavelength that varies and that depends on the type of wave. So to know what the frequency and wavelength of a particular wave. Will see how they are related to each other.

How are Frequency and Wavelength related?

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The frequency is how fast waves pass by a reference point in a second. Wavelength or Length of a Wave is the distance between crests. If the frequency is higher, the wavelength will be shorter. The length of an electromagnetic waveform, wavelength ($\lambda$) is always inversely proportional to its frequency (f), the number of cycles per second. As the frequency of the signal increases, the wavelength decreases.
Frequency and Wavelength
In general terms,
Frequency $\times$ wavelength = Speed of the wave
f $\lambda$ = v

Wavelength and Frequency Equation

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The frequency and wavelength relation is given by,
v = f $\lambda$
where,
v is speed of the wave,
f is the frequency,
$\lambda$ is the wavelength.

Wavelength and Frequency of Light

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Electromagnetic waves always travel with the same speed. Its the frequency and wavelength that varies in the different regions of the spectrum.If the light wave is having a wavelength of 4 meter and is going at a speed of 8 m/s then its frequency would be

f = $\frac{c}{\lambda}$
= $\frac{3 \times 10^8}{4\ m}$
= 7.5 $\times$ 107 Hz.

Wavelength and Frequency Problems

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Lets see some sample problems on wavelength and frequency:

Solved Examples

Question 1: Calculate the wavelength if the frequency is 450 KHz.
Solution:
 
Given: frequency = 450 kHz

The wavelength is given by,
$\lambda$ = $\frac{c}{f}$
$\lambda$ = $\frac{3 \times 10^8 m/s}{450 \times 10^3 Hz}$
$\lambda$ = 660 m.

 

Question 2: The light has a wavelength of 400 m. What is the frequency of the light?
Solution:
 
Speed of light = v = 3 $\times$ 108 m/s, Wave length $\lambda$ = 400 nm

The relation between frequency and wavelength is,
v = f $\lambda$

Frequency = f = $\frac{v}{\lambda}$
                     = $\frac{3 \times 10^8 m/s}{400 \times 10^{-9} m}$
                     = 75 $\times$ 104 Hz