Q 11-14-052JEE MainJEE Main 2023 (31 Jan, Shift 2)Easy
The displacement equations of two interfering waves are given by $y_1=10\sin\left(\omega t+\dfrac\pi3\right)$ cm, $y_2=5\left[\sin(\omega t)+\sqrt3\cos\omega t\right]$ cm respectively. The amplitude of the resultant wave is ______ cm.
Numerical value type. Enter your answer.
Answer: 20
$y_2=5\times2\left[\tfrac12\sin\omega t+\tfrac{\sqrt3}{2}\cos\omega t\right]=10\sin\left(\omega t+\dfrac\pi3\right)$.
The two waves are identical and in phase, so the resultant amplitude is $10+10=20\ \text{cm}$.
Solution by Sreeraj P, M.Sc Physics