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Wavelength

How wavelength is measured?

Wavelength can be measured by the distance between two successive maxima of a wave. It can be denoted by the symbol lambda (λ) and calculated by the formula λν = c, where ν = frequency and c = speed of the wave. Sound, light, water, and electromagnetic waves are the most common examples of waves whose wavelength depends on the medium where they are traveled. A sound wave depends on the air pressure where electromagnetic waves depend on the strength of the electric and magnetic fields. Generally, we use a photometer for the calculation of energy, wavelength, and frequency of light waves.

Wavelength calculation or measurement, symbol, formula to measure light spectrum or sound waves

The range of waves over which electromagnetic radiation exists is called the electromagnetic spectrum. Some commonly employed units such as meter (m), centimeter (cm), millimeter (mm), micrometer (μm), nanometer (nm), and angstrom (Å) are used for the calculation of the wavelength of the electromagnetic spectrum.

Frequency

The number of complete wavelength passing through a given point in unit time is called the frequency of radiation. It is denoted by the greek latter ν and measured by the unit reciprocal to time. Frequency is generally expressed in cycles per second or Hertz. The other units of frequency are kilocycle per second or kHz and megacycle per second or MHz.

Velocity wavelength frequency formula

At constant frequency, the velocity depends upon the medium through which the wave is passing. It is the unit of cm s-1 or m s-1. The product of wavelength and frequency is measured by the velocity of the wave in the medium. Therefore, wavelength (λ) × frequency (ν) = velocity (v).

When the density of the medium through which the wave is passing decreases, the wavelength and velocity of radiation increase. It reaches a constant or maximum value in a vacuum. Therefore, the velocity of light in a vacuum is denoted by the formula, c = λν, where, c = 3 × 108 m/s.

Sound waves

In physics, the sound is an acoustic wave that propagated through a medium such as a gas, liquid, or solid. The velocity of sound waves in air is 343 m/s at room temperature and atmospheric pressure. The wavelength of sound which is audible to the human ear is between 17 m to 17 mm. Some higher wavelength of a sound wave is used by bats to identify their targets. The speed and wavelength of sound waves depend on the medium where sound is travelers and the temperature of the medium. The speed of sound in a different medium is given below the table,

Medium Speed of sound (m/s)
Gases at 0°C and 1 atm pressure
air 343
carbon dioxide 258
carbon monoxide 337
oxygen 326
hydrogen 1270
Nitrogen 349
Liquids at 20 °C, 1 Atm pressure
ethanol 1160
mercury 1450
freshwater 1480
seawater 1540
Solid
Glass 5640
Lead 1960
Aluminum 5120
Steel 5960

Wavelength of light

The wavelength and frequency of uv-visible radiation of light in electromagnetic radiation

Radiation which we called light is the visible portion of the electromagnetic spectrum. It is lies between the wavelength 400 nm (violet) to 750 nm (red). Within the visible region, a person with normal color vision can be able to correlate the wavelength of light striking in the eye. The color of light corresponds to different wavelengths is given below the table,

Colour Wavelength (nm)
Violet 400 – 450
Blue 450 – 500
Green 500 – 570
Yellow 570 – 590
Orange 590 – 610
Red 610 – 750

We see that sunlight can be separated by passing through a prism into the light of many colors (red to violet). A light that contains a continuous sequence of colors varying from red to violet is called the continuous spectrum. Similarly, some light sources have a few colored lines separated by dark spaces is called line spectrum. Most of the line spectra are produced by atoms. Therefore, it is often called the atomic spectrum.

Calculating wavelength of light

The dual nature of light or electron was first proposed by the de Broglie equation in 1924. A light wave must have energy, wavelength, frequency, velocity, and amplitude. Experimentally, the velocity of all electromagnetic radiation is found to be the same 3 × 108 m/s in a vacuum. Again the bundle of energy emitted by light is called a photon. The wavelength and frequency of light can be measured by the following equation,

  • The velocity of light (c) = νλ
  • The energy of light (E) = hν

where, ν = frequency of light
λ = wavelength of light
h = Planck constant = 6.62607004 × 10-34 joule second.

The calculation or conversion of wavelength to frequency and energy of photons was suggested by Planck. According to him, if a photon energy E is emitted or absorbed with frequency = ν and wavelength = λ, E = hν = hc/λ. The Planck calculation suggests that a photon of long-wavelength has low energy and a photon of short wavelength has high energy. We use a photometer for calculating the energy of light, it can be converted to frequency or wavelength by the above formula.