Q 11-14-139JEE MainJEE Main 2025 (2 Apr, Shift 2)Medium
A sinusoidal wave of wavelength $7.5\ \text{cm}$ travels a distance of $1.2\ \text{cm}$ along the $x$-direction in $0.3\ \text{s}$. The crest P is at $x = 0$ at $t = 0$ s and the maximum displacement of the wave is $2\ \text{cm}$. Which equation correctly represents this wave?
Answer: (A) $y = 2\cos(0.83x - 3.35t)\ \text{cm}$
Wave speed: $v = \dfrac{1.2}{0.3} = 4\ \text{cm/s}$.
$k = \dfrac{2\pi}{\lambda} = \dfrac{2\pi}{7.5} \approx 0.84\ \text{cm}^{-1}$ and $\omega = vk = 4\times0.84 \approx 3.35\ \text{rad/s}$.
A crest at $x = 0$, $t = 0$ means $y = A$ there, which needs a cosine. The wave moves along $+x$, so
$$y = 2\cos(0.83x - 3.35t)\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics