Wavelength Formula: Definition, Wien's Law & Solved Examples

Wavelength is the distance between two consecutive points on a wave. The consecutive points refer to two points or particles in the same phase and are referred to as two crests or two troughs.

• Wavelength is expressed as the ratio of Wave Velocity to Frequency.
• Frequency and Wavelength are inversely proportional.
• The higher the frequency, the shorter the wavelength.
• Wavelength is denoted by the Greek letter lambda (λ).

Wavelength Formula is given as 

Here, λ refers to the Wavelength, v is the Wave Velocity, and f is the Frequency.

Key Terms: Wavelength, Wave, Frequency, Electromagnetic Waves, Lambda, Wave Velocity, Crests, Troughs, Wien's Displacement Law

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What is Wavelength?

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Wave refers to a dynamic disturbance that transfers energy from one point to another. In Physics, the two most important types of waves are Mechanical Waves and Electromagnetic Waves. 

• Wavelength refers to the distance between two consecutive crests or troughs of a wave. 
• These two consecutive crests or troughs have to be in the same phase.
• Crest is the high point of a wave while the trough is the low point of a wave. 
• In simpler words, Wavelength is the distance after which the shape of the wave repeats. 
• It is represented by lambda (\(\lambda\)).
• Wavelength is in an inverse relationship with Frequency. 
• The dimensional formula of Wavelength is [m⁰ l¹ t⁰].
• The SI unit of Wavelength is meter (m).

Wavelength

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Wavelength Formula

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Wavelength is the ratio of the Velocity of the Wave to Frequency. Wavelength Formula is as follows:

Where

• \(\lambda\) = Wavelength in m.
• v = Wave Velocity in m/sec.
• f = Frequency in Hz.

Read More: 

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Solved Examples on Wavelength Formula

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Given below are some solved examples of the Wavelength Formula:

Example 1: The speed of sound is around 340 m/s and the frequency of the wave crest is 20.0 cycles per second. Find the wavelength of the sound wave.

Solution: According to the question, 

• Frequency (f) = 20.0 cycles per seconds 
• Wave velocity (v) = 340 (m/s)

Using the Wavelength Formula, 

λ = v/f

λ = 340 / 20

λ = 17 m

So, the wavelength of the sound wave is 17 m.

Example 2: A motorboat creates waves while traveling across the surface of the sea. The waves travel towards the shores of the sea at a velocity of 1.50 m/s. and the distance between the wave crests is given as 2.0 m. What will be the frequency of the wave?

Solution: Given that

Velocity v = 1.50 m/s
Wavelength λ = 2.0 m

Using the Wavelength Formula, 

λ = v/f 

Rearranging the formula,

f = v/λ

f = 1.50/2.00

f = 0.75 waves/s

Therefore, the frequency of the wave is 0.75 waves per second.

What is Wavelength?

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Wien’s Displacement Law

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Wien's Displacement Law was given by the German Physicist Wilhelm Wein. The law states that the black-body radiation curve will peak at different wavelengths for different temperatures. These wavelengths are inversely proportional to the temperature. 

Where 

• \(\lambda\) (max) = Peak Wavelength 
• b = Wein’s Displacement Constant
• T = Absolute Temperature 

Wien’s Displacement Law

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Energy of Photon Formula

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Energy of a Photon can be determined through the Planck-Einstein Relation. Planck-Einstein Relation states that the energy E of a photon is directly proportional to its frequency. 

E ∝ v

E = hv

The frequency (v) can also be denoted as c/\(\lambda\). Therefore, 

Where 

• E = Energy of the Photon 
• h = Planck’s Constant 
• c = Speed of Light
• λ = Wavelength 

Also check: 

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Things to Remember 

• Wave is defined as a disturbance that travels through a medium from one location to another location.
• Wavelength is the distance between the two successive crests or troughs of a wave. 
• It is the distance over which the shape of the wave repeats.
• It is denoted by the symbol \(\lambda\) and is measured in meters (m).
• Wavelength is calculated as the ratio of Wave Velocity and Frequency.
• Wavelength Formula is given as \(\lambda\) = v / f.

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Previous Year Questions

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4. Wavelength of light of frequency 100 Hz… [NEET 1999]
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