Question

For superposition of two waves, which of the following is correct?
A. They must have the same frequency and wavelength.
B. They must have equal frequencies but may have unequal wavelengths.
C. They must have the same wavelengths but may have different frequencies.
D. They may have different wavelength and different frequencies

Answer 1

Hint: For this question, we have to understand the concept of the “Principle of superposition” for one or more waves travelling simultaneously in a medium. In simple words to understand with respect to waves, the principle of superposition represents the algebraic sum of the displacement travelled by each wave in the particular time and frequency.

Complete step by step answer:
The “Principle of Superposition” states that : -
When two or more waves arrive at a particular point in space, they are said to superimpose with each other and a new wave is formed in which the resultant displacement at any instant is equal to the vector sum of the displacements produced due to individual waves at that instant.
It also states that if a number of waves are travelling in a medium, then each one independently travels the shape and the characteristics of any wave are not changed due to the presence of other waves. For example, if the displacements of two waves, travelling simultaneously, is given by,
${{\text{y}}_1}\, = \,\,{{\text{f}}_1}\left( {{\text{t}}\, - \,\dfrac{{\text{x}}}{{\text{v}}}} \right)\,\,\,\,\,\,{\text{and}}\,\,\,\,\,{{\text{y}}_2}\, = \,\,{{\text{f}}_2}\left( {{\text{t}}\,{\text{ + }}\,\dfrac{{\text{x}}}{{\text{v}}}} \right)$
then, the displacement of the resultant superimposed wave is given by,
$${\text{y}}\,{\text{ = }}\,\,{{\text{y}}_{1\,}}\, + \,\,{{\text{y}}_2}$$
Where ${y_1}$ and ${y_2}$ are the displacements of the respective waves.
Hence, the wavelength and frequency depend only on the function $${{\text{f}}_1}\,{\text{and}}\,\,{{\text{f}}_2}$$. Therefore, these waves can have any wavelength and any frequency.
(D) option is correct.

Note: This principle of superposition holds not only for mechanical waves but also for electromagnetic waves. It holds for all types of waves, except for the waves of very large amplitude where amplitude is the maximum displacement travelled by wave in particular direction.