Question:
The phase difference between two particles of a medium lying between two consecutive nodes is:
The phase difference between two particles of a medium lying between two consecutive nodes is:
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In stationary waves, phase change between two consecutive nodes equals \(\pi\).
Updated On: Jul 18, 2026
- \(0\)
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{2}\)
- \(\pi\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding stationary waves between nodes.
In a stationary wave, the region between two consecutive nodes forms a single loop (or antinode region). All particles oscillate with same frequency but different phases depending on position.
Step 2: Phase difference concept in waves.
Phase difference between two points in a wave is: \[ \Delta \phi = \frac{2\pi}{\lambda} \Delta x \] This shows phase depends on separation distance between particles.
Step 3: Distance between two consecutive nodes.
Distance between two consecutive nodes is: \[ \frac{\lambda}{2} \] So one full node-to-node region corresponds to half wavelength.
Step 4: Phase change over half wavelength.
Since full wavelength corresponds to \(2\pi\) phase change, half wavelength corresponds to: \[ \pi \] Hence maximum phase variation in this region is \(\pi\).
Step 5: Interpretation for particles in region.
Particles between two nodes can have phase difference ranging from 0 to \(\pi\), depending on their position. Maximum possible phase separation is \(\pi\).
Step 6: Final conclusion.
Thus, required phase difference is: \[ \boxed{\pi} \]
In a stationary wave, the region between two consecutive nodes forms a single loop (or antinode region). All particles oscillate with same frequency but different phases depending on position.
Step 2: Phase difference concept in waves.
Phase difference between two points in a wave is: \[ \Delta \phi = \frac{2\pi}{\lambda} \Delta x \] This shows phase depends on separation distance between particles.
Step 3: Distance between two consecutive nodes.
Distance between two consecutive nodes is: \[ \frac{\lambda}{2} \] So one full node-to-node region corresponds to half wavelength.
Step 4: Phase change over half wavelength.
Since full wavelength corresponds to \(2\pi\) phase change, half wavelength corresponds to: \[ \pi \] Hence maximum phase variation in this region is \(\pi\).
Step 5: Interpretation for particles in region.
Particles between two nodes can have phase difference ranging from 0 to \(\pi\), depending on their position. Maximum possible phase separation is \(\pi\).
Step 6: Final conclusion.
Thus, required phase difference is: \[ \boxed{\pi} \]
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