Question

Two similar waves ' $x$ ' and ' $y$ ' of amplitude 'a' are moving in the same direction and superimposed. If the wave ' $y$ ' is lagging behind the wave ' $x$ ' by one-fourth of the cycle, then the amplitude of the resultant wave is equal to:

• (A) $a$
• (B) $\frac{a}{\sqrt{2}}$
• (C) $\sqrt{2}a$
• (D) None of these

Answer 1

The Correct Option is C

Explanation:
Given,$a_x=a_y=a$, and $\varphi =\frac{\pi }{2}$We know that when two similar waves are superimposed, the amplitude of the resultant wave is given as,$\Rightarrow A=2a\cdot \cos \frac{\varphi }{2}$$\Rightarrow A=2a\cdot \cos \frac{\pi }{4}$$A=\sqrt{2}a$Hence, the correct option is (C).