Question

Three coherent waves having amplitudes 12 mm, 6 mm and 4 mm arrive at a given point with successive phase difference of $\frac{\pi }{2}$. Then the amplitude of the resultant wave is:

• A. 7 mm
• B. 10 mm
• C. 5 mm
• D. 1.8 mm

Answer 1

Answer: (B)

10 mm

From the vector diagram,

$(A_{net}{)}_{13}=\sqrt{A_1^1+A_3^2+2A_1{A}_{3}cos\delta }$

$(A_{net}{)}_{13}=\sqrt{(12{)}^2+(4{)}^2+2\times 12\times 4\times cos{180}^0}=8mm$

Now the net amplitude,

$A_n=\sqrt{A_{13}^2+A_2^2+2A_2{A}_{13}cos{90}^0}=\sqrt{A_{13}^2+A_2^2}$

$A_n=\sqrt{(6{)}^2+(8{)}^2}=10mm$

The correct option is B.