 # Wavelength To Frequency Formula

The wavelength of any sinusoidal wave is defined as the spatial period of the wave, that is, the distance over the shape of the wave repeats itself. The wavelength is denoted by a Greek letter lambda (λ) and is calculated in the units of length or metre.

Frequency is defined as the number of time a recurring event occurs in one second. For a sinusoidal wave, we define frequency as the number of cycles or crest or trough completed in one second. Frequency is denoted by f or ν and is calculated in the units of Hertz.

As we know, for a sinusoidal wave moving at a fixed speed, the wavelength of the wave is inversely proportional to its frequency. Calculate the wavelength to frequency using BYJU’S online calculator.

## The Formula for Wavelength to Frequency

The wavelength to frequency formula is given by

Speed = Frequency x Wavelength

Wavelength = (Speed of the wave)/(Frequency of the wave)

As mentioned above, all the quantities are represented by a symbol. The symbolic representation of the formula given above can be seen as:

C = f × λ

In terms of wavelength to frequency, the formula is given as:

 $$\lambda =\frac{c}{f}$$

Where,

• λ is the wavelength of the wave under consideration expressed in the units of a metre,
• C is the speed of the wave in the given medium, expressed in terms of m/s
• f is the frequency of the wave expressed in terms of Hertz.

### Solved Examples

Example 1 In an experiment, the wavelength of a photon particle was observed to be 500 nm. What can be said about the frequency of the wave?

Solution: Given, the wavelength of the photon particle = 500 nm.
In order to calculate the frequency of the photon particle, we use the formula given above.

 $$f=\frac{c}{\lambda }$$

As we know, the speed of light is c = 3×108

Substituting the known values in the equation above, we get that,

$$f=\frac{3*10^{8}}{500*10^{-9}}$$

f=6×10-4 Hz

The frequency of the wave is equal to 6×10-4 Hz.

Example 2 For a light ray having a wavelength equal to 200 nm, calculate the frequency.

Solution: Given, the wavelength of the light ray = 200 nm. In order to calculate the frequency of the light ray, we use the formula given above.

 $$f=\frac{c}{\lambda }$$

As we know, the speed of light is c = 3×108.

Substituting the known values in the equation above, we get that,

$$f=\frac{3*10^{8}}{200*10^{-9}}$$

f=1.5×1014 Hz

The frequency of the wave is equal to 1.5×1014 Hz.