Question

Three waves of equal frequency having amplitudes $10\mu m$, $4\mu m$ and $7\mu m$ arrive at a given point with a successive phase difference of $\pi /2$. The amplitude of the resulting wave is $\mu m$ in given by

• A. $7$
• B. $6$
• C. $5$
• D. $4$

Answer 1

The correct option is C $5$

The wave $1$ & $3$ out of phase. Hence resultant phase difference between then is $\pi$

$\therefore$Resultant amplitude of $1$ & $3$=$10-7$=$3\mu m$

This wave has phase difference of $\frac{\pi }{2}$ with $4\mu m$

$\therefore$Resultant amplitude

$=\sqrt{3^2+4^2}=5\mu m$

Hence option (C) is correct