Wavelength is the distance travelled by a wave in one full cycle. It is a property of both travelling waves & standing waves. It is the distance between two adjacent corresponding points of the same phase on the wave, like two adjacent troughs, crests, or zero crossings. Since it is the distance travelled by a wave, the Dimensional Formula of Wavelength is equal to the Dimensional Formula of Length, which is
The Formula of Wavelength (λ) is expressed as
The Dimension of wavelength, as mentioned above, is that of Length.
The Dimensional Formula of Wavelength is as Follows
See Also:
A Dimensional Formula of a physical quantity, popularly known as a Dimension of a physical quantity, are mathematical expression denoting the dimensions of that quantity. In Physics, only a few quantities such as Length, Time, Charge, and Mass have a dimension of their own. Rest quantities have their dimensional formulae in terms of these basic dimensions.
The Dimensional formulae are used to understand the relationship between two or more physical quantities without using numerical quantities or actual equations. Each dimensional formula consists of a series of dimensions raised to the power of their occurrence. Dimensions are independent units used that measure the nature of a physical quantity.
A Dimensional Formula is expressed as follows:
Dimensional Formula: A Dimensional Formula is, as mentioned above, a mathematical formula of the Dimensions contained in a physical quantity.
Buckingham Pi Theorem: It is a theorem that states that when a physical quantity involves ‘n’ variables and ‘m’ fundamental dimensions, there will always be n – m dimensionless quantities that can express the relationship between the variables. These dimensionless quantities are called Pi terms and are used in reducing the number of variables required to describe a physical quantity.
Wavelength is an extremely important part of the wave which a student must thoroughly understand. However, to understand what wavelength is, you first need to understand what a wave is
A wave is a disturbance taking place in a medium changing its equilibrium. Unlike the usual disturbances, this disturbance is dynamic in nature, i.e. it gradually increases until the peak is reached and then decreases until the peak is reached in the opposite direction and then increases again until the peak is reached.
We are surrounded by waves. They come in numerous types. However, they can be classified into two broad types: mechanical waves and electromagnetic waves. Mechanical waves traverse in a physical medium, such as air, whereas electromagnetic waves traverse in spacetime. In other words, a mechanical wave disturbs a physical surrounding whereas an electromagnetic wave disturbs the fabric of spacetime. The most common waves around us are light and sound waves. Light is an electromagnetic wave whereas sound is a mechanical wave.
Waves can also be distinguished based on waveform. The waves can be sinusoidal, square, triangle, sawtooth etc. Most natural waves are sinusoidal waves, with a few exceptions such as ocean waves. Square, Triangle and Sawtooth waveforms are, on the other hand, used in musical instruments, electronic signals, etc.
In layman’s terms, wavelength is the measure of the length of a wave. However, it has many implications. The wavelength of a wave can determine its frequency, colour, energy etc. It is denoted by the Greek alphabet λ
Wavelength is defined as the distance travelled by a wave when it completes one full oscillation. In other words, it is the distance between a phase of a wave and the same phase of the succeeding wave. It is often depicted as the distance between two successive crests or two successive troughs.
Frequency and wavelength are inversely proportional to each other. The formula is given below
v=fλ
Where,
v is the speed of the wave
f is the frequency of the wave, and
λ is the wavelength of the wave
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