Q 11-14-116JEE MainJEE Main 2019 (10 Apr, Shift 2)Medium
The correct figure that shows, schematically, the wave pattern produced by the superposition of two waves of frequencies $9\ \text{Hz}$ and $11\ \text{Hz}$, is
Answer: (A) see figure
The superposition produces beats with beat frequency $11 - 9 = 2\ \text{Hz}$, so the amplitude envelope repeats every $0.5\ \text{s}$:
$$y = 2A\cos(2\pi t)\,\sin(2\pi\cdot10\,t)$$
The envelope $|2A\cos 2\pi t|$ is maximum at $t = 0, 0.5, 1, 1.5, 2\ \text{s}$ and zero at $t = 0.25, 0.75, \ldots$, giving four loops between $0$ and $2\ \text{s}$. This is figure (1).
Solution by Sreeraj P, M.Sc Physics