Q 11-14-093JEE MainJEE Main 2021 (26 Aug, Shift 2)Medium
Two waves are simultaneously passing through a string and their equations are: $y_1 = A_1\sin k(x - vt)$, $y_2 = A_2\sin k(x - vt + x_0)$. Given amplitudes $A_1 = 12$ mm and $A_2 = 5$ mm, $x_0 = 3.5$ cm and wave number $k = 6.28$ cm$^{-1}$. The amplitude of resulting wave will be ______ mm.
Numerical value type. Enter your answer.
Answer: 7
Phase difference $\phi = kx_0 = 6.28\times3.5 = 7\pi$, equivalent to $\pi$: the waves are in opposite phase.
$$A = \sqrt{A_1^2 + A_2^2 + 2A_1A_2\cos\phi} = |A_1 - A_2| = 12 - 5 = 7\ \text{mm}$$
Solution by Sreeraj P, M.Sc Physics