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Distance between two consecutive nodes or antinodes from the equation of a stationary wave

The same question, asked 3 times: May 2022 S1*, 4 May 2023 S2*, 14 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    May 2022 S1

    5
    A stationary wave is represented by y=10sin⁡(πx4)cos⁡(20πt)y = 10\sin\left(\frac{\pi x}{4}\right)\cos(20\pi t) where xx and yy are in cm and tt in second. The distance between two consecutive nodes is

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  2. Question 2

    4 May 2023 S2

    8
    A stationary wave is represented by y=12cos⁡(π6x)sin⁡(8πt)y = 12\cos\left(\frac{\pi}{6}x\right)\sin(8\pi t), where xx and yy are in cm and tt in second. The distance between two successive antinodes is

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  3. Question 3

    14 May 2026 S2

    123
    The equation of a stationary wave along a stretched string is y=5sin⁡πx3cos⁡40πty = 5\sin\dfrac{\pi x}{3}\cos 40\pi t where xx and yy are in cm and tt in second. The separation between two adjacent nodes is

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