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Wavelength for which the maximum particle speed is a given multiple of the wave speed

The same question, asked 2 times: 29 Jun 2022*, 26 Jul 2022. Every wording below, oldest first.

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  1. Question 1

    29 Jun 2022

    16
    A longitudinal wave is represented by x=10sin⁡2π(nt−xλ)cmx = 10\sin2\pi\left( nt -\frac{x}{\lambda} \right)cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:

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  2. Question 2

    26 Jul 2022

    103
    A transverse wave is represented by y=2sin⁡(ωt−kx) cmy = 2\sin(\omega t - kx)\ cm. The value of wavelength (in cmcm ) for which the wave velocity becomes equal to the maximum particle velocity, will be;

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