Two transverse sinusoidal waves travel in opposite directions along a string of length 3m whose both ends are fixed. The speed of transverse waves in the string is 0.5 cm/s. Each has an amplitude of 3 cm and wavelength of 6 cm. The equation for the resulting wave is 

If the components waves are $y_1=asin(kx-\omega t)$ and $y_2=asin(kx+\omega t)$ then their superposition gives rise to a standing wave. 

If both ends of the string are attached to rigid boundaries, the equation of standing wave is $y=2a sinkx.cos\omega t$, such that at x = 0, y is zero for all values of t.

Here, $a=3cm, \lambda =6cm\Rightarrow K=\frac{2\pi }{6}c{m}^{-1}=\frac{\pi }{3}c{m}^{-1}$

Also, $\frac{\omega }{K}=V\Rightarrow \omega =0.5\times \raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right. \raisebox{1ex}{$rad$}\!\left/ \!\raisebox{-1ex}{$s$}\right.=\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.\raisebox{1ex}{$ rad$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

$\therefore$ The equation of resulting wave is $y=6 \sin \frac{\pi x}{3}\cos \frac{\pi t}{6}$

option (1) is wrong as at $x=0$, y is not zero for all values of t.