 # Unit of Wavelength

## What are Waves?

A wave is a theoretical representation of the propagation of energy in a medium or vacuum. This energy is also termed as disturbances which travel in a particular medium be it solid, liquid or gas. Eg- Sound energy. There are few energies that do not require any medium to travel and thus can travel in vacuum. Eg- Light energy.

Graphical Representation of Waves

The propagation of energy or disturbances can be shown in a graph where the x-axis represents the distance travelled by the disturbance and y-axis represents the time taken to travel a particular distance.

Example : A sound wave (mechanical wave) travelling in a medium. Displacement is taken on the y-axis and measured in metres whereas time is taken on the x-axis and measured in seconds. (image will be uploaded soon)

Crest : It is the part of waves lying above the x-axis. Also termed as heights.

Trough : It is the part of waves lying below the x-axis. Also termed as depressions.

Amplitude : It is the maximum displacement from the central position (x-axis) to one of its extreme position (highest point of a crest or lowest point of a trough)

Period : It is the time taken for one complete wave to pass through a point. One complete wave consists of one crest and one trough.

Frequency : It is the number of waves passing through a point in one sec.

Wavelength : It is the displacement between two successive crests or troughs.

Wavelength and Its Unit

Wavelength is the length of a wave from the highest point of a crest to the highest point of the adjacent crest or the lowest point of a trough to the lowest point of adjacent trough. It is denoted by a symbol called Lambda (λ). As per the given definition, we know that wavelength is the length thus the S.I unit of wavelength should be the same as the S.I unit of length. We know, the S.I unit of length is metre so the SI unit of wavelength is also metre.

Definitions of Metre:

Metre Can be Defined in Different Ways:

• In terms of prototype meter bar: To maintain the new metric standard of length ‘International Bureau of Weights and Measures’ constructed and preserved a prototype metre bar. This bar is made up of alloy (90% platinum and 10% iridium). One metre is the distance measured between two lines on this bar at zero degree. In other words, the length of this bar is taken as 1 metre.

• In terms of the distance between latitude: Meter is one ten-millionth of the maximum distance between the Equator and the North pole. Distance between equator and North pole is 10,000 km. The unit Kilometre is derived from the metre. Kilo means 1000 times thus 1 kilometre is equal to 1000 metres.

• In terms of light: One meter is the distance travelled by light in a vacuum in 1/299,792,458 second. A metre is measured by the speed of light because

1.  It remains constant everywhere.

2.  It can be measured from anywhere in the world to get an accurate and same result.

• In terms of thermionic emission: Krypton-86 atom in a vacuum emits orange-red electromagnetic radiation of a particular wavelength. Meter is defined as 1650 763.73 wavelengths of the radiation emitted by Krypton-86.

Other Units of Wavelengths:

As discussed earlier the SI unit of wavelength is metre. Some wavelengths are short and some are long. Even to solve different numerical problems the larger and the smaller units length was required. Thus we use exponential powers of 10 to measure the large property whereas the negative exponential is used for the measurement of shorter wavelengths.

Examples-

Submultiple Units : decimeter, centimetre, millimetre, etc

Multiple Units : decameter, kilometre, gigameter, etc.

Below is the table showing the relation of a metre with its multiple and submultiple units.

## Multiples & Submúltiplos of SI Units - The Metre

 Multiples Submultiples Value Symbol Name Value Symbol Name 103 m Km Kilometre 10-1 m dm Decimetre 106 m Mm Megametre 10-2 m cm Centimetre 109 m Gm Gigametre 10-3 m mm Millimetre 1012 m Tm Terametre 10-6 m μm Micrometre 1015 m Pm Petametre 10-9 m nm Nanometre

The Relationship Between Wavelength and Frequency

Wavelength is the length of a wave and frequency is the number of waves. Thus in a unit area, if the length of a wave increases then its frequency decreases and if the length of a wave decreases then its frequency increases. This means that the wavelength and frequency are inversely proportional to each other.

Since the frequency of waves are measured in large units so wavelength (because it is inversely proportional to frequency) is measured in smaller units.

Wavelengths of Different Waves in Metres

Gamma Rays : The wavelength of gamma rays is the shortest. Its is less than 0.001 nanometer or 10-12 metres.

X-rays : The wavelengths of X rays are in the range of 0.001 - 10 nm.

Ultraviolet : The wavelength of ultraviolet rays are in the range of 10 - 400 nm.

Visible Light : The wavelength of visible lights are in the range of 400-700 nm.

Infrared : The measure of the wavelength of infrared rays ranges from 700 nm  to 1 mm.

Radio Waves : The wavelength of radio waves is the longest. Its is longer more than 1 millimetre or 0.001 metres.