Q 11-14-091JEE MainJEE Main 2021 (26 Aug, Shift 1)Easy
Two travelling waves produce a standing wave represented by equation $y = (1.0\ \text{mm})\cos\left[(1.57\ \text{cm}^{-1})x\right]\sin\left[(78.5\ \text{s}^{-1})t\right]$. The node closest to the origin in the region $x > 0$ will be at $x = $ ______ (in cm).
Numerical value type. Enter your answer.
Answer: 1
Nodes occur where $\cos(1.57x) = 0$. The first one for $x > 0$:
$$1.57x = \frac{\pi}{2} \Rightarrow x = \frac{1.57}{1.57} = 1\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics