Two travelling waves ${y_1} = A\sin [k(x - ct)]$ and ${y_2} = A\sin [k(x + ct)]$ are superimposed on a string. The distance between adjacent nodes is

Standing waves are produced in a string $16 \ m$ long. If there are $9$ nodes between the two fixed ends of the string and the speed of the wave is $32 \ m/s$, what is the frequency of the wave (in $Hz$)?

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

$A$ standing wave having $3$ nodes and $2$ antinodes is formed between two atoms having a distance of $1.21 \ Å$ between them. The wavelength of the standing wave is (in $Å$)

Stationary waves are produced in a $10\,m$ long stretched string. If the string vibrates in $5$ segments and the wave velocity is $20\,m/s$,the frequency is ..... $Hz$.

In a stationary wave,which of the following statements is correct regarding strain?