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Read the speed, frequency or wavelength from a travelling-wave equation

This type of question, asked 9 times: 28 Jul 2022, 24 Jan 2023, 10 Apr 2023, 11 Apr 2023, 8 Apr 2024, 23 Jan 2025, 4 Apr 2025, 2 Apr 2026 S1, 5 Apr 2026 S1. All 9 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    28 Jul 2022

    9
    In the wave equation
    y=0.5sin⁡2πλ(400t−x)my = 0.5\sin\frac{2\pi}{\lambda}(400t - x)m
    the velocity of the wave will be:

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  2. Question 2

    24 Jan 2023

    18
    A travelling wave is described by the equation
    y(x,t)=[0.05sin⁡(8x−4t)]my(x,t) = \lbrack 0.05\sin(8x - 4t)\rbrack m
    The velocity of the wave is: [all the quantities are in SI unit]

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  3. Question 3

    10 Apr 2023

    26
    A transverse harmonic wave on a string is given by y(x,t)=5sin⁡(6t+0.003x)y(x,t) = 5\sin(6t + 0.003x) where xx and yy are in cmcm and tt in sec. The wave velocity is__ ms−1ms^{- 1}.

  4. Question 4

    11 Apr 2023

    23
    The equation of wave is given by
    Y=10−2sin⁡2π(160t−0.5x+π4)Y =10^{- 2}\sin2\pi\left( 160t - 0.5x +\frac{\pi}{4} \right)
    Where xx and YY are in mm and tt in ss. The speed of the wave is___ kmh−1kmh^{- 1}

  5. Question 5

    8 Apr 2024

    95
    A plane progressive wave is given by y=2cos⁡2π(330t−x)my= 2\cos2\pi(330t-x)m. The frequency of the wave is:

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  6. Question 6

    23 Jan 2025

    79
    The equation of a transverse wave travelling along a string is y(x,t)=4.0sin⁡[20×10−3x+600t]mmy(x,t) = 4.0\sin\left\lbrack 20 \times10^{- 3}x + 600t \right\rbrack mm, where x is in the mm and t is in second. The velocity of the wave is :

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  7. Question 7

    4 Apr 2025

    93
    Displacement of a wave is expressed as x(t)=5cos⁡(628t+π2)mx(t) = 5\cos\left( 628t+\frac{\pi}{2} \right)m. The wavelength of the wave when its velocity is 300 m/s300\text{ }m/s is :

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  8. Question 8

    2 Apr 2026 S1

    10
    The equation of a plane progressive wave is given by y=5cos⁡π(200t−x150)y= 5\cos\pi\left( 200t-\frac{x}{150} \right) where xx and yy are in cm and tt is in second. The velocity of the wave is ____\_\_\_\_ m/sm/s

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  9. Question 9

    5 Apr 2026 S1

    23
    A transverse wave on a string is described by y=3sin⁡(36t+0.018x+π/4)y = 3\sin(36t + 0.018x + \pi/4). Where x,yx,y are in cm and tt in seconds. The least distance between the two successive crests in the wave is ____\_\_\_\_ cm. (Nearest integer) (π=3.14)(\pi = 3.14)