One end of a taut string of length 3m along the x axis is fixed at x = 0.The speed of the waves in the string is $$100 ms^{-1}$$. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is(are)

A

$$y(t) = A \sin \frac{\pi x}{6} \cos \frac{50 \pi t}{3}$$

B

$$y(t) = A \sin \frac{\pi x}{3} \cos \frac{100 \pi t}{3}$$

C

$$y(t) = A \sin \frac{5 \pi x}{6} \cos \frac{250 \pi t}{3}$$

D

$$y(t) = A \sin \frac{5 \pi x}{2} \cos {250 \pi t}$$