Question

Two sound waves (expressed in CGS units) given by $y_{1} = 0.3\sin\frac{2\pi}{\lambda}(vt - x)$ and $y_{2} = 0.4\sin\frac{2\pi}{\lambda}(vt - x + \theta)$ interfere. The resultant amplitude at a place where phase difference is $\pi/2$ will be

• A. 0.7 cm
• B. 0.1 cm
• C. 0.5 cm
• D. $\frac{1}{10}\sqrt{7}cm$

Answer 1

Answer: (C)

0.5 cm

Answer 2

Resultant amplitude

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

= $\sqrt{0.3^{2} + 0.4^{2} + 2 \times 0.3 \times 0.4 \times \cos\frac{\pi}{2}}$= $0.5cm$