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Reading the wave velocity or frequency off a progressive wave equation

This type of question, asked 6 times: 10 May 2024 S2, 11 May 2024 S1, 12 May 2024 S2, 13 Apr 2026 S2, 16 Apr 2026 S1, 14 May 2026 S2. All 6 questions below, oldest first.

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  1. Question 1

    10 May 2024 S2

    49
    The equation of wave is Y=6sin⁡ ⁣(12πt−0.02πx+π3)Y=6\sin\!\left(12\pi t-0.02\pi x+\frac{\pi}{3}\right) where 'xx' is in m and 'tt' in s. The velocity of the wave is

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  2. Question 2

    11 May 2024 S1

    48
    A transverse wave Y=2sin⁡(0.01x+30t)Y = 2\sin(0.01x + 30t) moves on a stretched string from one end to another end in 0.5 second. If x and y are in cm and t in second, then the length of the string is

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  3. Question 3

    12 May 2024 S2

    21
    The equation of wave motion is Y=5sin⁡(10πt−0.02x+π3)Y = 5\sin\left(10\pi t - 0.02x + \frac{\pi}{3}\right) where xx is in metre and tt in second. The velocity of the wave is

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  4. Question 4

    13 Apr 2026 S2

    125
    A traveling wave is described by the equation y(x,t)=[0.05sin⁡(8x−4t)]y(x, t) = [0.05\sin(8x - 4t)] m The velocity of the wave is [All the quantities are in SI unit]

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  5. Question 5

    16 Apr 2026 S1

    124
    The equation of wave motion is Y=6sin⁡(12πt−0.02πx+π3)Y = 6\sin\left(12\pi t - 0.02\pi x + \dfrac{\pi}{3}\right) where x is in metre and time in second. The velocity of the wave is

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  6. Question 6

    14 May 2026 S2

    121
    The equation of a plane progressive wave is Y=0.025sin⁡(100t+0.25x)Y = 0.025\sin(100t + 0.25x). The frequency of this wave would be

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