A transverse wave is represented by y = 2sin (ω t - kx) cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be: (a) 4 π (b) 2 π (c) π (d) 2

Answer: (a). Wave velocity (ω)/(k) = (ωλ)/(2π); maximum particle velocity = Aω Equal when λ = 2π A = 2π(2) = 4π cm So the answer is (a) 4π.

A transverse wave is represented by y = 2sin (ω t - kx) cm. The value… | JEE Main 2022 (26 Jul, Shift 2)

Q64JEE Main 2022 · 26 JUL · SHIFT 2Medium

Progressive Wave Equation

A transverse wave is represented by $y = 2\sin(\omega t - kx)\text{ cm}$ . The value of wavelength (in $\text{cm}$ ) for which the wave velocity becomes equal to the maximum particle velocity, will be:

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Answer: (a)

Wave velocity $\frac{\omega}{k} = \frac{\omega\lambda}{2\pi}$ ; maximum particle velocity $= A\omega$
Equal when $\lambda = 2\pi A = 2\pi(2) = 4\pi\text{ cm}$
So the answer is (a) $4\pi$ .

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