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Distance between two points at a given phase difference on the wave y = A sin(wt + kx)

The same question, asked 3 times: 10 May 2024 S2*, 14 May 2024 S1*, 15 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    10 May 2024 S2

    30
    A simple harmonic progressive wave is represented by y=Asin⁡(100πt+3x)y=A\sin(100\pi t+3x). The distance between two points on the wave at a phase difference of π3\frac{\pi}{3} radian is

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  2. Question 2

    14 May 2024 S1

    4
    A progressive wave is given by Y=12sin⁡(5t−4x)Y=12\sin(5t-4x). On this wave, how far away are the two points having a phase difference of 90∘90^\circ?

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  3. Question 3

    15 Apr 2026 S2

    121
    A simple harmonic progressive wave is represented by y=Asin⁡(120πt+3x)y = A\sin(120\pi t + 3x). The distance between two points on the wave at a phase difference of π3\dfrac{\pi}{3} radian is

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