Question

Three waves of equal frequency having amplitudes $10 \, mm$ , $4 \, mm$ , and $7 \, mm$ arrive at a given point with a successive phase difference of $\frac{\pi }{2}$ , the amplitude of the resulting wave in mm is given by

• A. $7$
• B. $6$
• C. $5$
• D. $4$

Answer 1

Answer: (C)

As phase difference between waves of amplitudes $10 \, mm$ and $7 \, mm$ is $\pi $ , therefore, their resultant amplitude $=10-7=3 \, mm$ .
Now amplitudes $3 \, mm$ and $4 \, mm$ have a phase difference $ \, =\frac{\pi }{2}$ .
$\therefore $ Resultant amplitude $=\sqrt{3^{2} + 4^{2}}=5 \, mm$