Progressive Wave Equation question from JEE Main 2025 (2 Apr, Shift 2)

Answer: (a)

1. $v = \frac{1.2}{0.3} = 4\text{ cm/s}$, $k = \frac{2\pi}{7.5} = 0.83\text{ cm}^{-1}$
2. $\omega = kv = 0.838 \times 4 \approx 3.35\text{ rad/s}$
3. Crest at $x = 0$, $t = 0$ means $y = A$ there, so use cosine; travelling along $+x$ gives $(kx - \omega t)$.
4. So the answer is (a) $y = 2\cos(0.83x - 3.35t)\text{ cm}$.