Question

Two waves of equal amplitude ${x_0}$ and equal frequency travel in the same direction in a medium. The amplitude of the resultant wave is
A. 0
B. ${x_0}$
C. $2{x_0}$
D. Between 0 and $2{x_0}$

Answer 1

Hint: In this question, we need to determine the amplitude of the resultant wave such that the two waves of equal amplitude ${x_0}$ and equal frequency travel in the same direction. Since the amplitude of both the waves are the same and both are moving in the same direction through the same medium so by the principle of superposition their relative amplitude adds up.

Complete step by step answer:
Given the amplitude of the two waves \[ = {x_0}\]
We know that when two waves of equal amplitude and equal frequency travel in the same direction in a medium then their amplitude adds up; hence by applying the principle of superposition we can say the amplitude of the resultant wave is equal to \[R = {x_1} + {x_2}\] where, \[x_1\] and \[x_2\] are the position of the waves.
Now from the above equation we can say the amplitude of the resultant wave will be minimum when the amplitude of both the waves is zero and it will be maximum when the amplitude of both the waves is ${x_0}$.
\[\therefore R = {x_0} + {x_0} = 2{x_0}\]
Therefore, the amplitude of the resultant wave traveling in the same direction in a medium will be between 0 and \[2{x_0}\].

So, the correct answer is “Option D”.

Note:
It is worth down here that the amplitude and the frequency of a wave are equal to each other. The amplitude of a wave decreases when frequency of the wave increases. Moreover, frequency signifies the rate of repetition of the wave between the fixed points and is measured in hertz (Hz).