Q 11-14-069JEE MainJEE Main 2022 (24 Jun, Shift 1)Easy
The equations of two waves are given by:
$$y_1 = 5\sin 2\pi(x - vt)\ \text{cm}$$
$$y_2 = 3\sin 2\pi(x - vt + 1.5)\ \text{cm}$$
These waves are simultaneously passing through a string. The amplitude of the resulting wave is:
Answer: (A) $2\ \text{cm}$
Phase difference $\phi = 2\pi\times 1.5 = 3\pi$, so the waves are in opposite phase ($\cos\phi = -1$).
$$A = \sqrt{A_1^2 + A_2^2 + 2A_1A_2\cos\phi} = |5 - 3| = 2\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics