Question:
Equations of a stationary and a travelling waves are as follows: \(y_1 = a\sin kx\cos\omega t\) and \(y_2 = a\sin(\omega t - kx)\). The phase difference between two points \(x_1 = \dfrac{\pi}{3k}\) and \(x_2 = \dfrac{3\pi}{2k}\) are \(\phi_1\) and \(\phi_2\) respectively for two waves. The ratio \(\dfrac{\phi_1}{\phi_2}\) is
Equations of a stationary and a travelling waves are as follows: \(y_1 = a\sin kx\cos\omega t\) and \(y_2 = a\sin(\omega t - kx)\). The phase difference between two points \(x_1 = \dfrac{\pi}{3k}\) and \(x_2 = \dfrac{3\pi}{2k}\) are \(\phi_1\) and \(\phi_2\) respectively for two waves. The ratio \(\dfrac{\phi_1}{\phi_2}\) is
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In a stationary wave, all points between two consecutive nodes are in phase ($\phi=0$), and points in adjacent segments are out of phase ($\phi=\pi$). For a travelling wave, $\phi = k\Delta x$.
Updated On: Apr 20, 2026
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
For a stationary wave, the phase difference between two points depends on whether they are in the same or opposite loops. For a travelling wave, phase difference \(= k\Delta x\).
Step 2: Detailed Explanation:
Separation: \(\Delta x = x_2 - x_1 = \dfrac{3\pi}{2k} - \dfrac{\pi}{3k} = \dfrac{7\pi}{6k}\). Neither point is a node. For stationary wave, points in the same segment (between consecutive nodes at \(x=0,\pi/k\)): \(x_1 = \pi/(3k)\) is in first segment; \(x_2 = 3\pi/(2k)\) is in second segment. Points in adjacent segments have phase difference \(\phi_1 = \pi\). For travelling wave: \(\phi_2 = k\Delta x = \dfrac{7\pi}{6}\). Ratio: \(\dfrac{\pi}{7\pi/6} = \dfrac{6}{7}\).
Step 3: Final Answer:
\(\dfrac{\phi_1}{\phi_2} = \dfrac{6}{7}\).
For a stationary wave, the phase difference between two points depends on whether they are in the same or opposite loops. For a travelling wave, phase difference \(= k\Delta x\).
Step 2: Detailed Explanation:
Separation: \(\Delta x = x_2 - x_1 = \dfrac{3\pi}{2k} - \dfrac{\pi}{3k} = \dfrac{7\pi}{6k}\). Neither point is a node. For stationary wave, points in the same segment (between consecutive nodes at \(x=0,\pi/k\)): \(x_1 = \pi/(3k)\) is in first segment; \(x_2 = 3\pi/(2k)\) is in second segment. Points in adjacent segments have phase difference \(\phi_1 = \pi\). For travelling wave: \(\phi_2 = k\Delta x = \dfrac{7\pi}{6}\). Ratio: \(\dfrac{\pi}{7\pi/6} = \dfrac{6}{7}\).
Step 3: Final Answer:
\(\dfrac{\phi_1}{\phi_2} = \dfrac{6}{7}\).
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