Question

The dimensions of wavelength is:
$A)\text{ }\left[ {{M}^{0}}{{L}^{0}}{{T}^{0}} \right]$
$B)\text{ }\left[ {{M}^{0}}L{{T}^{0}} \right]$
$C)\text{ }\left[ {{M}^{0}}{{L}^{-1}}{{T}^{0}} \right]$
D) None of these

Answer 1

Hint: The wavelength of a wave is nothing but the distance travelled by the wave in one time period. It can also be defined as the distance between two successive crests or two successive troughs in a wave. Therefore, we can derive its dimensions by understanding the dimensions of distance.

Complete step-by-step answer:
The wavelength of a wave is one of its characteristic parameters. It is the distance that the wave travels in one time period or the separation between two successive crests or two successive troughs.
Therefore, it can be said that since the wavelength of a wave is essentially a measure of distance, it must have the same dimensions as that of distance.
Now, the dimensions of distance are that of length, that is, $\left[ {{M}^{0}}L{{T}^{0}} \right]$.
Therefore, going by this explanation, the dimensions of wavelength will also be $\left[ {{M}^{0}}L{{T}^{0}} \right]$.

So, the correct answer is “Option B”.

Additional Information: Usually when a wave travels from one medium to another, its wavelength changes. Since the speed of the wave can be written mathematically as the product of its wavelength and frequency, the speed of the wave also changes for different media. However, it must also be noted that the frequency of the wave remains the same in different media.

Note: Students should not get confused between the wavelength and the wave number. The wave number of the wave is the number of cycles that it completes or the number of wavelengths present in a unit distance. It can be written as the inverse of the wavelength and hence, will have dimensions that are inverse to the wavelength, that is of length inverse $\left[ {{M}^{0}}{{L}^{-1}}{{T}^{0}} \right]$.