Progressive Wave Equation question from MHT CET 2026 (20 Apr, Shift 2)

Answer: (c)

1. From the figure: $y_1 = a_1\sin\left(\omega t - \frac{2\pi x}{\lambda}\right)$, $y_2 = a_2\cos\left(\omega t - \frac{2\pi x}{\lambda} + \frac{\pi}{6}\right)$.
2. $y_2 = a_2\sin\left(\omega t - \frac{2\pi x}{\lambda} + \frac{\pi}{6} + \frac{\pi}{2}\right)$, so $\Delta\phi = \frac{2\pi}{3}$.
3. Path difference $= \frac{\lambda}{2\pi} \times \frac{2\pi}{3} = \frac{\lambda}{3}$
4. So the answer is (c) $\frac{\lambda}{3}$.