Question

Three waves of amplitudes $12\mu m$, $4\mu m$ and $9\mu m$ but of same frequency arrive at a point in a medium with a successive phase diffeerence of $\frac{\pi }{2}$. Then the resultant amplitude is

• A. $4$
  
• B. $7$
  
• C. $5$
  
• D. $25$
  

Answer 1

The correct option is C $5$

Since three waves have a successive phase difference of $\pi /2$.
So, first and third waves have phase difference of $\pi$.
Thus, net amplitude of first and third wave is $A_1=12-9=3\mu m$
Amplitude of second wave $A_2=4\mu m$
Resultant amplitude $A_R=\sqrt{A_1^2+A_2^2}$
$\therefore$ $A_R=\sqrt{3^2+4^2}=5\mu m$