IB Physics SL Theme C: Wave behaviour questions

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Question 1

Multiple choiceEasy1 mark

A string supports a standing wave. Points P and Q are antinodes immediately on opposite sides of the same displacement node. What is the phase difference between the oscillations of P and Q, in radians?

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Answer: C. Adjacent antinodes separated by a displacement node oscillate in antiphase: when one is at maximum positive displacement, the other is at maximum negative displacement. This is a half-cycle separation, so Δϕ=2π(1/2)=π rad\Delta\phi = 2\pi(1/2) = \pi\ \text{rad} A: treats the two points as oscillating in phase. B: assigns a quarter-cycle separation instead of opposite-phase motion. D: assigns a three-quarter-cycle separation instead of a half-cycle. Remember: antinodes in neighbouring segments separated by a node oscillate in antiphase.

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