Question

When two sound waves with a phase difference of $\pi/2$ and each having amplitude A and frequency $\omega$are superimposed on each other, then the maximum amplitude and frequency of resultant wave is

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

Answer 1

Answer: (D)

$\sqrt{2}A;\omega$

Answer 2

Resultant Amplitude = $\sqrt{{a_{1}}^{2} + {a_{2}}^{2} + 2a_{1}a_{2}\cos\varphi}$ =

$\sqrt{\mathbf{A}^{\mathbf{2}}\mathbf{+}\mathbf{A}^{\mathbf{2}}\mathbf{+ 2}\mathbf{A}^{\mathbf{2}}\mathbf{\cos}\frac{\mathbf{\pi}}{\mathbf{2}}}$= $\sqrt{\mathbf{2}}\mathbf{A}$

and frequency remains same = ω.