Dimensional Formula of Wavelength

According to the definition of Wavelength, it is the distance present between two successive crests of the curve. The specific distance present between two consecutive peaks present in a wave is called a Wavelength. To better understand the concept, we have discussed aspects associated with Wavelength and the dimensional formula of Wavelength. Also, go through the dimensional formula of wavelength questions to better understand the topic. 

What is Wavelength?

Wavelength is defined as the specific distance present between two successive troughs or crests in a curve. When analysed in a high-frequency wave, the distance between the trough is lesser than the troughs present in a low-frequency wave and vice versa.

Discovery of Wavelength.

Sir William Herschel first studied waves while he was working with the quantity of heat present in various colours of visible light. He conducted extensive experiments using a glass prism to degrade white light into consecutive colours. After that, he placed thermometers under specific colours after the range of red light. He found out that white light had the maximum temperature and found the aspects of infrared waves. Depending on this discovery, later on, scientists found other varieties of waves.

What are the components of a wave?

The following are the components we can find in a wave.

• Rest position: the undisturbed position of particles when they are not vibrating. If we plot a graph, the X-axis is considered to be the rest position.
• Crest: the elevated point of the wave which starts from the rest point is called a crest.
• Trough: the dropped position of the wave from the rest position is called the trough.
• Displacement: the entire wave, from the starting point to the end, is called displacement.
• Amplitude: the specific distance between a crest or a trough of a wave from its resting position is the measurement of amplitude.
• Wavelength: the specific distance between two successive crests or troughs is called the Wavelength.
• Frequency: the total number of waves that pass via a point per second is the wave’s frequency. It is calculated in Hertz.

How can Wavelength be calculated?

If we divide the velocity of the wave by its frequency, we can find the measurement of the Wavelength. This relationship is critical to understanding the dimensional formula of Wavelength.

So, Wavelength = wave velocity/frequency.

λ= v/f where λ= distance between the two considered crests and troughs in metres, v= velocity of the speed of the particular wave, and f = frequency of the particular wave calculated in Hertz.

Dimensional formula of Wavelength.

The dimensional formula of Wavelength is presented as M0L1T0.

Here, M= the mass, L= length and T= time.

Derivation:

Wavelength is the calculated distance between two points (crests or troughs) of two adjacent waves. 

So, wavelength = distance between the two considered points on a waveform.

So the dimensional formula of Wavelength can be represented as M0L1T0.

What is the frequency?

The number of oscillations made by a wave per unit time is considered as the frequency of that wave and is calculated in Hertz. When the Wavelength between two crests or troughs is short, the frequency is high, whereas when the Wavelength is long, the frequency is low.

What is the relationship between frequency and Wavelength?

There lies a quintessential connection between frequency and Wavelength. The frequency and Wavelength are considered to be inversely proportional to each other. The wave with the highest frequency will have the smallest Wavelength and vice-versa.

So, the bigger the energy, the bigger the frequency and the shorter the Wavelength. So,  shorter wavelengths are more powerful than longer ones.

Conclusion

When studying the dimensional formula of Wavelengths, it is important to know in detail about the wavelengths. You can follow the dimensional formula of wavelength notes to get a better idea about the concept as well. The topic of Wavelength is extensive, and we have tried to cover the maximum here; you can go through dimensional wavelength notes and dimensional wavelength questions as well to get a wider concept of the topic. Dimensional Formulae has the following advantages: To check whether a formula is dimensionally correct or not. To convert units from one system to another. To derive relations between physical quantities based on their interdependence.