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Question #42070
The Question
A river flows uniformly with velocity in the direction. A wave generator produces plane surface waves that travel with a phase speed relative to the water. The waves travel downstream and reflect normally off a stationary vertical pier at . The superposition of the incident and reflected waves creates an interference pattern consisting of a stationary spatial envelope and a propagating carrier wave. A swimmer swims downstream with a velocity relative to the river. What is the velocity of the swimmer relative to the phase velocity of the carrier wave?
Options
- A.
- B.
- C.
- D.
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Intuition_Breaker
Train your brain to resist "obvious" answers that are designed to deceive your intuition.
Concepts Behind This Question
Rain-Man/Swimmer Logic|Boundary Condition Reflection|Small Angle Approximation
Why This Question Is Tricky
Common Mistakes
This question tests the application of the superposition principle and Galilean transformations in a dynamic wave medium.
Students commonly fall into the trap of assuming that a standing wave formed in a moving medium either drifts at the medium's velocity () or remains perfectly stationary relative to the ground ().
They fail to recognize that the differing wavelengths of the incident and reflected waves (due to the Doppler-like effect of the moving medium against a stationary boundary) create an interference pattern where the spatial nodes are fixed, but the internal carrier wave propagates at a highly non-intuitive phase velocity.
By blindly applying static formulas, they miss the dynamic phase-shift at the boundary.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Motion in a Plane - Class 11 Part 1 |
| Concept | Rain-Man/Swimmer Logic |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |