Frequency and Wavelength - Definition, Wavelength of Light, Examples, FAQ

Q: If the wavelength of a photon is given to be 200nm, find the frequency of the wave.

c=λf=>f=c/λ=3×10 8 / (200×10 -9 )Hz=1.5×10 14 Hz

Edited By Vishal kumar | Updated on Jul 02, 2025 05:01 PM IST

When we talk about waves, it may be a transverse wave like light or a longitudinal wave like sound, we come across some terms which are inevitably connected with the wave motion. These are- frequency and wavelength of a wave, time period, amplitude, phase, angular frequency, wave number, angular wave number and so on. However in this article we will mainly discuss frequency and wavelength of a wave in detail along with the other concepts. We will also discuss about ’what is frequency of a wave?’, ‘what is wavelength of a wave?’, ‘wavelength and frequency relationship’, ‘what is wavelength and frequency of light?’, ‘ numericals based on frequency-wavelength relation’, ‘factors affecting frequency and wavelength of a light wave’, ‘frequency of light’ and ‘ energy and wavelength relationship’. But first let us understand ‘what is a wave?’ and ‘what are the types of waves?’.

Frequency and Wavelength - Definition, Wavelength of Light, Examples, FAQ

Wave and its classifications

Before understanding the concept of frequency and wavelength of a wave in detail, let us first define the wave.

A wave can be considered as a disturbance that propagates in space which transports energy and momentum from one point of space to another without actual transport of matter.

For example, we consider sound wave motion. When we talk to someone, we actually create disturbance in the air close to our lips. Energy is then transferred to the air particles of this region by either pushing or pulling them. These disturbed particles exert force on the neighboring particles and so on and thus transfer this disturbance from our lips to the other person’s ear without actually transferring any particle from our lips to the other person’s ear.

Classification of waves can be done on the basis of –

Classification of waves

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What is wavelength of a wave?

Wavelength of a wave (denoted by lambda λ) is the distance travelled by the wave when one particle of the medium completes one vibration about its mean position or can be defined as the distance between nearest particles of the medium, vibrating in the same phase.

Consider a transverse wave (see figure-1)

Distance between consecutive crests and troughs is called wavelength. (Fig-1)

A crest is a point of the medium, which is raised above the normal position of rest of the particles of the medium while a trough is opposite to crest which is a minimum point of the wave. The wavelength of the wave in this case is the distance between two consecutive crests or troughs.

However, in case of longitudinal waves, particles produce regions of compression (high pressure) and rarefaction (low pressure) and the wavelength in this case is the distance between two consecutive compressions or two consecutive rarefactions.

Unit of wavelength is the same as distance i.e. meter in S.I. unit.

Wave number- Denoted by ѵ,It is defined as the number of waves per unit length of a wave pattern. It is clearly reciprocal of the wavelength of the given wave.

$\Rightarrow \bar{v}=\frac{1}{\lambda}$ (Equation-1)

Angular wave number- Denoted by k, it is product of 2π with 1/λ . Thus,

=>k= 2π× 1/λ (Equation-2)

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What is frequency of a wave?

Frequency is defined as the number of periodic motions executed by a body or a particle per second. It is denoted by ν (or n or f). Hence, number of vibrations or number of complete wavelengths by a particle in 1 second is frequency of a wave (see figure-2)

oscillations per second is called frequency. (Fig-2)

Unit of frequency is hertz denoted by Hz. Hence, 1Hz=1 oscillation per second= 1 cps= 1s^-1.

Remember that frequency may not be necessarily an integer.

Now, Time period (T) is the time taken by the wave to travel a distance equal to one wavelength. Hence, it is the least interval of time after which the periodic motion of a body repeats itself (see figure-3).

Figure showing time period of a wave (Fig-3)

Unit of time period is second. Thus, clearly the frequency of a wave is reciprocal of time period.

ν=1/T (Equation-3)

Angular frequency of a body which executes periodic motion is nothing but equals to the product of frequency of the body with factor 2π. It is denoted by ω.

Thus, ω=2π×ν=2π/T

=>ω =2π/T (Equation-4)

S.I. unit of angular frequency is rad/s.

NCERT Physics Notes:

Relationship between wavelength and frequency

Since speed equals distance by time, therefore v=λ/T, where λ is the wavelength and T is the time period.

Wavelength and frequency relation can be written as-

V=λν (Equation-5)

=>speed= lambda×frequency

Wavelength and frequency of light

If speed of light is denoted by c, then by equation-5 we can write-

C= λ/T (Equation-6)

Now, we already know that speed of light is measured to be almost equal to 3×10⁸m/s. Then if we are given either the time period or frequency of the light we are considering, we can calculate the wavelength of light and similarly if we know the wavelength of light we are using, we can calculate frequency. Thus equation-6 also describes the wavelength and frequency relation in case of electromagnetic waves.

The table below shows electromagnetic spectrum arranged by their respective frequency and wavelength. Their photon energies are also specified.

Table showing spectrum of EM waves with their respective wavelengths,frequencies and photon energies

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Factors affecting frequency and wavelength of a light wave

Both wavelength and velocity of a light wave can change but the frequency of the light wave always stays the same. When an electromagnetic wave enters a denser medium such as glass, its velocity decreases by a factor of the refractive index of that medium (n). Since frequency of an electromagnetic wave never changes, its wavelength is bound to change to account for the change in its velocity. Thus, lower the velocity of the electromagnetic wave is, the shorter its wavelength will be. This can be clearly seen by equation-5 where, if we keep the frequency constant, the velocity of the electromagnetic wave is directly proportional to its wavelength. The above case is nothing but the phenomenon of refraction of light (see figure-4). This is one of the many ways by which we can change the wavelength or velocity of an electromagnetic wave.

Fig shows how E.M. wave velocity and wavelength change with change in medium. (Fig-4)

Wavelength and energy relationship
Wien's radiation law and Raleigh-Jean law tried to establish wavelength and energy relationship but the former one came up with an empirical formula that was only true for lower wavelengths and the later one came up with an equation which was only true for larger wavelengths or lower frequencies. The vice versa for both of these equations gave random and wrong values. Thus, Planck solved this problem by modifying classical mechanics and laying the basis for Quantum Mechanics. He found a whole new equation which states that energy emitted or absorbed from radiation at frequency ν is equal to nhν, n=1, 2,...

That implies, emission or absorption of energy can be in multiples of hν.

Thus, wavelength and energy relationship can be written as-

E=nhv, where h=Planck’s constant. If n=1, E=hν (Equation-6)

E=nhc/λ (Equation-7) 5×10¹⁴s^-1

The above equation is strictly for photons in electromagnetic waves. However, we know that light has dual nature i.e. both wave and particle nature. Thus, for matter waves, de broglie found the equation as-

λ=h/P, where P is the momentum of the particle present in the wave and lambda is its wavelength. (Equation-7)

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Frequently Asked Questions (FAQs)

1. If the wavelength of a photon is given to be 200nm, find the frequency of the wave.

c=λf=>f=c/λ=3×10⁸ / (200×10^-9)Hz=1.5×10¹⁴Hz

2. In the phenomena of reflection of light, does the wavelength change?

No, reflection of light doesn’t change its wavelength.

3. Find frequency and wavelength of 1 kev photon.

By equation-7, λ=hc/E = 12.4kevÅ/1kev ( as hc=12.4kevÅ)

=>λ=12.4Å

Now,f=c/ λ=3×10⁸/12.4×10^-10m =2.42×10¹⁴Hz

4. Write the relationship between energy of photons and angular frequency.

From equation-6 and equation-4, E=hω/2π

5. What is the relationship between frequency and wavelength?

Frequency and wavelength are inversely related. As frequency increases, wavelength decreases, and vice versa. This relationship is described by the wave equation: wave speed = frequency × wavelength. For a given wave speed, if frequency goes up, wavelength must go down to maintain the same product.

6. Can two waves have the same frequency but different wavelengths?

Yes, but only if they are traveling through different media. The speed of a wave depends on the medium it's traveling through. Since wave speed = frequency × wavelength, if two waves have the same frequency but are traveling at different speeds (in different media), they will have different wavelengths.

7. How does changing the frequency of a wave affect its energy?

Increasing the frequency of a wave increases its energy. This is because the energy of a wave is directly proportional to its frequency. Higher frequency waves, like X-rays and gamma rays, carry more energy than lower frequency waves, like radio waves.

8. Why do we see different colors of light?

We see different colors of light because they have different wavelengths. Each wavelength in the visible spectrum corresponds to a specific color. For example, red light has a longer wavelength than blue light. Our eyes detect these different wavelengths and our brain interprets them as distinct colors.

9. What happens to the wavelength of light when it enters a denser medium?

When light enters a denser medium, its wavelength decreases. This is because the speed of light decreases in a denser medium, but its frequency remains constant. Since wave speed = frequency × wavelength, if speed decreases and frequency stays the same, wavelength must decrease.

10. What is the difference between mechanical and electromagnetic waves in terms of wavelength?

Mechanical waves, like sound, require a medium to propagate and their wavelength is the distance between two consecutive compressions or rarefactions. Electromagnetic waves, like light, can travel through vacuum, and their wavelength is the distance between two consecutive crests or troughs of the oscillating electric and magnetic fields.

11. What is the difference between wavelength and amplitude?

Wavelength is the distance between two consecutive crests or troughs of a wave, while amplitude is the maximum displacement of the wave from its equilibrium position. Wavelength determines the type or "color" of the wave (in the case of light), while amplitude determines the intensity or "brightness" of the wave.

12. How does the wavelength of radio waves compare to that of visible light?

Radio waves have much longer wavelengths than visible light. While visible light wavelengths range from about 380 to 700 nanometers, radio waves can have wavelengths from a few millimeters to hundreds of meters long.

13. How does wavelength affect the diffraction of waves?

Diffraction is more pronounced for waves with longer wavelengths. When a wave encounters an obstacle or opening, the amount of bending (diffraction) depends on the ratio of the wavelength to the size of the obstacle or opening. Longer wavelengths diffract more around obstacles and through openings of a given size.

14. What is the significance of the de Broglie wavelength?

The de Broglie wavelength relates the wave-like properties of particles to their momentum. It suggests that all matter exhibits wave-like properties, with the wavelength inversely proportional to the particle's momentum. This concept is fundamental to quantum mechanics and explains phenomena like electron diffraction.

15. What is the relationship between wavelength and the energy of a photon?

The energy of a photon is inversely proportional to its wavelength. This relationship is described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is wavelength. Shorter wavelengths correspond to higher energy photons.

16. How does wavelength affect the refraction of light?

Different wavelengths of light refract (bend) at different angles when passing from one medium to another. This is because the refractive index of a material depends on the wavelength of light. Generally, shorter wavelengths (like blue light) refract more than longer wavelengths (like red light), which causes dispersion phenomena like rainbows.

17. What is the relationship between wavelength and the resolution of optical instruments?

The resolution of optical instruments, such as microscopes and telescopes, is limited by the wavelength of light used. Shorter wavelengths allow for higher resolution (ability to distinguish finer details) because they can resolve smaller objects or closer points. This is why electron microscopes, which use electrons with very short de Broglie wavelengths, can achieve much higher resolution than light microscopes.

18. How does wavelength relate to the photoelectric effect?

The photoelectric effect depends on the wavelength (or frequency) of incident light, not its intensity. Light below a certain wavelength (above a certain frequency) can eject electrons from a metal surface. This threshold wavelength depends on the work function of the metal. Shorter wavelengths (higher frequencies) result in ejected electrons with higher kinetic energy.

19. What is the significance of the Compton wavelength?

The Compton wavelength is a quantum mechanical property of a particle, equal to the wavelength of a photon whose energy is the same as the rest mass energy of the particle. It plays a role in Compton scattering, where photons interact with charged particles, and is important in understanding quantum electrodynamics.

20. How does wavelength relate to the uncertainty principle?

The uncertainty principle states that we cannot simultaneously know the exact position and momentum of a particle. For waves, this translates to an uncertainty relationship between wavelength and position. The more precisely we know the wavelength of a wave, the less precisely we can know its position, and vice versa.

21. How does wavelength affect the efficiency of solar cells?

Solar cells are designed to absorb light of specific wavelengths efficiently. The bandgap of the semiconductor material in a solar cell determines which wavelengths can be effectively converted to electricity. Photons with wavelengths corresponding to energies below the bandgap are not absorbed, while those with much higher energies lose some energy as heat.

22. How does wavelength affect the penetration depth of electromagnetic waves in conductors?

The penetration depth (or skin depth) of electromagnetic waves in conductors is related to the wavelength. Generally, higher frequency (shorter wavelength) waves penetrate less deeply into a conductor than lower frequency (longer wavelength) waves. This phenomenon, known as the skin effect, is important in the design of electrical systems and RF shielding.

23. What is the relationship between wavelength and the resolving power of a diffraction grating?

The resolving power of a diffraction grating is its ability to separate closely spaced wavelengths. It increases with the number of lines in the grating and the order of diffraction. For a given grating, shorter wavelengths can be resolved with greater precision than longer wavelengths.

24. What is the significance of the Planck wavelength?

The Planck wavelength is the scale at which quantum effects of gravity become significant. It's extremely small (about 1.6 × 10^-35 meters) and represents a theoretical limit to the measurement of length. Below this scale, our current understanding of physics breaks down, and a theory of quantum gravity would be needed.

25. How does wavelength affect the scattering of X-rays in crystallography?

In X-ray crystallography, the wavelength of the X-rays must be comparable to the spacing between atoms in the crystal for effective diffraction to occur. The relationship between the wavelength, the angle of scattering, and the spacing between crystal planes is described by Bragg's law. Different wavelengths can reveal different aspects of the crystal structure.

26. What is the relationship between wavelength and the refractive index of a material?

The refractive index of a material generally varies with the wavelength of light, a phenomenon known as dispersion. For most transparent materials, the refractive index decreases as wavelength increases. This relationship is described by the Cauchy equation or more complex models like the Sellmeier equation.

27. What is the significance of the de Broglie wavelength in electron microscopy?

In electron microscopy, the de Broglie wavelength of the electrons determines the resolution limit of the microscope. Electrons accelerated to high velocities have very short de Broglie wavelengths, much shorter than visible light, allowing electron microscopes to achieve much higher resolution than optical microscopes.

28. How does wavelength relate to the quantum mechanical description of atomic orbitals?

In quantum mechanics, atomic orbitals are described by wave functions. The de Broglie wavelength of the electron is related to its momentum and energy, which in turn determine the shape and size of the orbital. Different orbitals (s, p, d, f) correspond to different standing wave patterns of the electron around the nucleus.

29. What is the relationship between wavelength and the band structure of solids?

In solid-state physics, the wavelength of electrons (described by their de Broglie wavelength) interacts with the periodic potential of the crystal lattice. This interaction leads to the formation of allowed and forbidden energy bands. The relationship between electron wavelength and lattice spacing determines the electronic and optical properties of the material.

30. How does wavelength affect the design of optical fibers?

The wavelength of light used in optical fibers affects their performance in several ways. It determines the amount of dispersion (spreading of pulses), attenuation (loss of signal strength), and the number of modes that can propagate. Most modern optical fibers are designed to operate at specific wavelengths (e.g., 1310 nm or 1550 nm) where attenuation and dispersion are minimized.

31. What is the significance of the Compton wavelength in particle physics?

The Compton wavelength is a fundamental property of particles that relates their rest mass to a corresponding wavelength. It plays a role in quantum electrodynamics and sets a scale at which quantum effects become important for a particle. For electrons, it's about 2.43 × 10^-12 meters, while for protons it's much smaller due to their larger mass.

32. What is the relationship between wavelength and the quantum tunneling effect?

Quantum tunneling is related to the wave nature of particles, described by their de Broglie wavelength. The probability of tunneling through a potential barrier depends on the wavelength of the particle wave function compared to the width of the barrier. Particles with shorter wavelengths (higher energy) generally have a higher probability of tunneling.

33. How does the wavelength of light affect its ability to penetrate materials?

Generally, shorter wavelengths of light have higher energy and can penetrate materials more easily than longer wavelengths. For example, X-rays (very short wavelength) can pass through soft tissue, while visible light (longer wavelength) cannot. However, this relationship is not always linear and depends on the specific material properties.

34. How does the Doppler effect relate to wavelength?

The Doppler effect describes the change in observed frequency (and thus wavelength) of a wave when there is relative motion between the source and the observer. When the source moves towards the observer, the observed wavelength decreases (frequency increases). When the source moves away, the observed wavelength increases (frequency decreases).

35. How does the wavelength of light affect its scattering in the atmosphere?

Shorter wavelengths of light scatter more in the atmosphere than longer wavelengths. This phenomenon, known as Rayleigh scattering, explains why the sky appears blue during the day (blue light scatters more) and why sunsets appear red (red light scatters less and travels further through the atmosphere).

36. What is the significance of the wavelength in interference patterns?

The wavelength of light determines the spacing of interference patterns. In constructive interference, waves combine to produce a larger amplitude when the path difference is an integer multiple of the wavelength. In destructive interference, waves cancel out when the path difference is an odd multiple of half the wavelength.

37. What is meant by the "characteristic wavelength" of an atom?

The characteristic wavelength refers to the specific wavelengths of light that an atom can emit or absorb. These wavelengths correspond to the energy differences between electron energy levels in the atom. When an electron transitions between energy levels, it emits or absorbs a photon with a wavelength determined by the energy difference.

38. How does the concept of wavelength apply to matter waves?

Matter waves, proposed by de Broglie, suggest that particles can exhibit wave-like properties. The wavelength of a matter wave is given by the de Broglie equation: λ = h/p, where h is Planck's constant and p is the particle's momentum. This concept is crucial in quantum mechanics and explains phenomena like electron diffraction.

39. What is the relationship between wavelength and the color of visible light?

In the visible spectrum, different wavelengths correspond to different colors. Longer wavelengths (around 620-750 nm) appear red, while shorter wavelengths (around 380-450 nm) appear violet. The full spectrum of visible light includes all colors between these extremes, with green light in the middle (around 495-570 nm).

40. How does wavelength affect the transmission of electromagnetic waves through the atmosphere?

Different wavelengths of electromagnetic radiation are absorbed or transmitted differently by the atmosphere. For example, visible light passes through relatively easily, while much of the ultraviolet spectrum is blocked by the ozone layer. Radio waves can pass through the atmosphere, but some frequencies are reflected by the ionosphere.

41. What is the relationship between wavelength and the energy levels in a quantum well?

In a quantum well, electrons are confined in one dimension, leading to quantized energy levels. The allowed wavelengths of the electron's wave function in the well are related to these energy levels. Shorter wavelengths correspond to higher energy levels, similar to the relationship between wavelength and energy for photons.

42. What is the significance of the Bragg wavelength in fiber optic communications?

In fiber optic communications, the Bragg wavelength is the wavelength of light that is strongly reflected by a fiber Bragg grating. This property is used to create wavelength-specific reflectors, filters, and sensors in optical fibers. The Bragg wavelength depends on the spacing of the grating and the refractive index of the fiber.

43. How does the concept of wavelength apply to standing waves?

In standing waves, the wavelength is related to the length of the medium in which the wave exists. For example, in a string fixed at both ends, the fundamental wavelength is twice the length of the string. Higher harmonics have wavelengths that are integer fractions of this fundamental wavelength.

44. How does wavelength affect the operation of a laser?

The wavelength of a laser is determined by the energy transitions in the lasing medium. It affects many aspects of laser operation, including the focusing ability (shorter wavelengths can be focused to smaller spots), the interaction with materials (absorption, reflection, and transmission depend on wavelength), and the suitability for specific applications.

45. How does wavelength affect the operation of antennas?

The wavelength of electromagnetic radiation is crucial in antenna design. The size and geometry of an antenna are often related to the wavelength of the signals it's designed to transmit or receive. For example, a half-wave dipole antenna has a length equal to half the wavelength of the signal. Different wavelengths require different antenna designs for optimal performance.

46. How does wavelength affect the operation of photonic crystals?

Photonic crystals are designed to affect the propagation of light based on its wavelength. They have a periodic structure with features comparable to the wavelength of light. This structure creates photonic band gaps - ranges of wavelengths that cannot propagate through the crystal. The specific wavelengths affected depend on the crystal's structure and materials.

47. What is the significance of the Wien displacement law in relation to wavelength?

Wien's displacement law relates the temperature of a black body to the wavelength at which it emits the most radiation. As the temperature increases, the peak wavelength of emission shifts to shorter wavelengths. This law explains why hotter objects appear bluer (emit more short-wavelength light) and cooler objects appear redder.

48. How does wavelength relate to the concept of group velocity in wave propagation?

Group velocity is the velocity at which the overall shape of a wave's amplitudes propagates through space. It's related to how the wavelength changes with frequency (the dispersion relation). In a dispersive medium, different wavelengths travel at different speeds, which can lead to pulse spreading in communication systems.

49. What is the relationship between wavelength and the operation of quantum cascade lasers?

Quantum cascade lasers are designed to emit light at specific wavelengths, typically in the mid- to far-infrared range. The wavelength of emission is determined by the energy level transitions in the carefully designed quantum well structures within the laser. By adjusting the thickness of these layers, the emission wavelength can be tuned.

50. How does wavelength affect the design of metamaterials?

Metamaterials are engineered to have properties not found in nature, often by manipulating electromagnetic waves. The structures in metamaterials are typically smaller