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Ratio of the maximum particle velocity to the wave velocity of a progressive wave

This type of question, asked 7 times: 9 May 2024 S2, 11 May 2024 S2, 13 May 2024 S2, 22 Apr 2025 S1, 23 Apr 2025 S1, 19 Apr 2026 S2, 12 May 2026 S1. All 7 questions below, oldest first.

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  1. Question 1

    9 May 2024 S2

    4
    The equation of simple harmonic progressive wave is given by y=asin⁡2π(bt−cx)y = a\sin 2\pi(bt - cx). The maximum particle velocity will be half the wave velocity, if c=c =

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  2. Question 2

    11 May 2024 S2

    49
    A transverse wave in a medium is given by y=Asin⁡2(ωt−kx)y = A\sin^2(\omega t - kx). It is found that the magnitude of the maximum velocity of particles in the medium is equal to that of the wave velocity. What is the value of A?

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  3. Question 3

    13 May 2024 S2

    45
    The equation of a progressive wave is Y=asin⁡2π ⁣(nt−x5)Y=a\sin 2\pi\!\left(nt-\frac{x}{5}\right). The ratio of maximum particle velocity to wave velocity is

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  4. Question 4

    22 Apr 2025 S1

    43
    The equation of wave is y=60sin⁡(1200t−6x)y= 60\sin(1200t- 6x), where ' yy ' is in micron, ' tt ' is in second and ' xx ' is in metre. The ratio of maximum particle velocity to the wave velocity of wave propagation is

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  5. Question 5

    23 Apr 2025 S1

    5
    A particle performs S.H.M. of amplitude 'A' and wavelength ' λ\lambda ', Then the velocity of the wave (V) and the maximum particle velocity (v) are related as

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  6. Question 6

    19 Apr 2026 S2

    123
    The equation of a progressive wave is given by y=6cos⁡(100t−4x)y = 6\cos(100t - 4x) where yy is in μm\mu\mathrm{m}, xx in metre and tt in second. The ratio of the maximum particle velocity to the velocity of wave is

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  7. Question 7

    12 May 2026 S1

    121
    A simple harmonic progressive wave is given by the equation y=asin⁡2π(nt−xλ)y = a\sin 2\pi\left(nt - \dfrac{x}{\lambda}\right). If the wave velocity is equal to 16×\dfrac{1}{6} \times (maximum particle velocity), then the wavelength λ\lambda is {a\{a = amplitude, nn = frequency, tt = time, yy = displacement, xx = distance}\}

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