Question

Two sound waves having same amplitude 'A' and angular frequency '$\omega$' but having a phase difference of $(\frac{\pi}{2})^c$ are superimposed then the maximum amplitude of the resultant wave is

• A. $\frac{A}{\sqrt{2}}$
• B. $\frac{A}{2}$
• C. $\sqrt{2} A$
• D. $2 A$

Answer 1

Answer: (C)

$\sqrt{2} A$

Answer 2

When two waves of amplitude $A$ and phase difference $\frac{\pi}{2}$ superimpose, the resultant amplitude $R$ is given by

$$R = \sqrt{A^2 + A^2 + 2A^2\cos\left(\frac{\pi}{2}\right)}$$

Since $\cos\left(\frac{\pi}{2}\right) = 0$,

$$R = \sqrt{2A^2} = \sqrt{2}A.$$

Thus, the maximum amplitude of the resultant wave is $\sqrt{2}A$.