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Wavelength Frequency Formula

The wavelength is the property of a wave which is the distance between identical points between two successive waves. The distance between one crest of one wave and the next one is the wavelength of the wave. In equations, the wavelength is indicated using the Greek letter \(\lambda\). In this article, we will discuss the relationship between wavelength and frequency of a wave. Also, we will see the Wavelength frequency formula with an example. Let us learn it!

Wavelength Frequency Formula

Concept of wavelength:

The wavelength of light determines the colour whereas the wavelength of the sound determines the pitch. The wavelengths of visible light may extend from about 700 nm to 400 nm. The wavelength of audible sound range from about 17 mm to 17000 mm. Thus wavelengths of audible sound are much longer than those of visible light.

The wavelength of any sinusoidal wave can be defined as the spatial period of the wave. This is the distance over the shape of the wave repeats itself. We calculate the wavelength in the units of length or meter.

Frequency is defined as the number of times for a recurring event occurs in one second. Thus for a sinusoidal wave, we define frequency as the number of cycles completed in one second. We denote frequency by f or ν and calculate it in the units of Hertz or Hz.

As we know, for a sinusoidal wave moving with a constant speed, the wavelength of the wave is inversely proportional to its frequency. Thus, the wavelength to frequency formula is:

Speed = Frequency × Wavelength

i.e. Wavelength=\( \frac {(Speed of the wave)}{(Frequency of the wave)} \)

The symbolic representation of this formula and the formula is as follows:

\(\lambda = \frac {c}{f} \)


\(\lambda\) is the wavelength of the wave under consideration expressed in the units of a meter
c is the speed of the wave in the medium and expressed in terms of \(ms^{-1}\)
f is the frequency of the wave. And it is expressed in terms of Hertz.


Solved Examples 

Q.1: In an experiment in physics, the wavelength of a photon particle was observed to be 500 nm. What will be the frequency of the wave?

Solution: As given here, the wavelength of the photon particle = 500 nm.

i.e. \(\lambda = 500 nm\)

i.e. \(\lambda = 500 \times 10^{-9} m \)

Also speed of light,

C = \(3\times 10^8 m s{-1}\)

In order to calculate the frequency of the photon particle, we will use the formulas:

\(\lambda = \frac {c}{f} \)

Rearrangingn the formula,

f = \(\frac {c}{\lambda}\)

= \(\frac {3\times 10^8}{500 \times 10^{-9}}\)

= \(6 \times 10 ^{14} Hz \)

Q.2: For a light ray which have the wavelength equal to 200 nm, calculate the frequency of the ray.

Solution: As given, in the problem,

Wavelength of the light ray = 200 nm

\(\lambda = 200 \times 10^{-9} m \)

Also speed of light,

C = \(3 × 10^8 m s{-1} \)

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

\(\lambda = \frac {c}{f} \)

Rearranging the formula,

f = \(\frac {c}{\lambda}\)

= \(\frac {3\times 10^8}{200 \times 10^{-9}}\)

= \(1.5 \times 10^{14} Hz. \)

The frequency of the wave is equal to \(1.5 \times 10^{14} Hz.\)

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