One end of a taut string of length $3 \ m$ along the $x$-axis is fixed at $x=0$. The speed of the waves in the string is $100 \ m/s$. 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):
$(A)$ $y(x,t) = A \sin \frac{\pi x}{6} \cos \frac{50 \pi t}{3}$
$(B)$ $y(x,t) = A \sin \frac{\pi x}{3} \cos \frac{100 \pi t}{3}$
$(C)$ $y(x,t) = A \sin \frac{5 \pi x}{6} \cos \frac{250 \pi t}{3}$
$(D)$ $y(x,t) = A \sin \frac{5 \pi x}{2} \cos 250 \pi t$

• A
  $(A, B, C)$
• B
  $(A, B, D)$
• C
  $(A, C, D)$
• D
  $(B, C, D)$