$A$ standing wave having $3$ nodes and $2$ antinodes is formed between two atoms having a distance of $1.21 \; \mathring{A}$ between them. The wavelength of the standing wave is .... $\mathring{A}$

What kind of waves can survive as standing waves?

$A$ stretched string is fixed at both ends. It is made to vibrate so that the total number of nodes formed in it is '$x$'. The length of the string in terms of the wavelength of waves formed in it is $(\lambda = \text{wavelength})$

The correct statement about stationary waves is that

Two progressive waves are travelling towards each other with velocity $50 \,m/s$ and frequency $200 \,Hz$. The distance between two consecutive antinodes is (in $\,m$)

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):
$(A)$ $y(x,t) = A \sin \frac{\pi x}{6} \cos \frac{50 \pi t}{3}$
$(B)$ $y(x,t) = A \sin \frac{\pi x}{3} \cos \frac{100 \pi t}{3}$
$(C)$ $y(x,t) = A \sin \frac{5 \pi x}{6} \cos \frac{250 \pi t}{3}$
$(D)$ $y(x,t) = A \sin \frac{5 \pi x}{2} \cos 250 \pi t$