Q: A transverse wave is described by the equation y = y_{0} sin 2π (ft -x/λ ). The maximum particle velocity is equal to four times the wave velocity if

(a) λ = πy_{0}/4

(b) λ = πy_{0}/2

(c) λ = πy_{0}

(d) λ = 2πy_{0}

Ans: (b)

Sol: Wave velocity $\large v = \frac{\omega}{k}= \frac{2\pi f}{2\pi/\lambda} = f \lambda$

Maximum Particle velocity $\large v_{pmax} = \omega A = 2\pi f y_0$

$\large 2\pi f y_0 = 4 (f \lambda)$

$\large \lambda = \frac{\pi y_0}{2}$