Question

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

• A. 5
• B. 6
• C. 3
• D. 4

Answer 1

The correct option is A 5

$Y_1=10\sin \omega \times t$,

$Y_2=4\sin (\omega \times t+\pi /2)=4\cos \omega \times t$,

$Y_3=7\sin (\omega \times t+\pi )=-7\sin \omega \times t$

by the law of superposition of waves,

$Y=Y_1+Y_2+Y_3=3\sin \omega \times t+4\cos \omega \times t=5\sin (\omega \times t+\varphi )$

here,

$\varphi ={\cos }^{-1}3/5={\sin }^{-1}4/5$