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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.
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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.
In general terms,
Frequency $\times$ wavelength = Speed of the wave
f $\lambda$ = v
f $\lambda$ = v
v = f $\lambda$
where, v is speed of the wave,
f is the frequency,
$\lambda$ is the wavelength.
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. 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
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,
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