Question

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

• A. 7 mm
• B. 10 mm
• C. 5 mm
• D. 4.8 mm

Answer 1

The correct option is B 10 mm

Since, it is given that the waves arrive at the same point with a phase difference of $\pi /2$

Therefore, the waves having an amplitude of 12mm and 4 mm are completely out of phase, and then their resultant amplitude is 12 - 4 = 8mm

Now, the 8mm and 6mm waves are ${90}^o$ out of phase so, their resultant amplitude would be given by Pythagorus theorem

$A^2=6^2+8^2$

Therefore, A = 10 mm