The displacement of a particle in a string stretched in the $X$ direction is represented by $y$. Among the following expressions for $y$,which ones describe wave motion?

$A$ massless rod is suspended by two identical strings $AB$ and $CD$ of equal length. $A$ block of mass $m$ is suspended from point $O$ such that $BO$ is equal to $x$. Further,it is observed that the frequency of the $1^{st}$ harmonic (fundamental frequency) in $AB$ is equal to the $2^{nd}$ harmonic frequency in $CD$. Then,the length of $BO$ is:

$A$ stretched uniform wire of length $L$ under tension $T$ is vibrating with fundamental frequency $n$. $A$ closed pipe of the same length $L$ is also vibrating with the same fundamental frequency $n$. If the tension $T$ is increased by $16 \,N$, the wire resonates with the $2^{\text{nd}}$ harmonic of the same closed pipe. The initial tension in the wire is: (in $\,N$)

$A$ wire of linear mass density $\mu = 9.8 \times 10^{-3} \, kg \, m^{-1}$ passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of $30^{\circ}$ with the horizontal. Masses $m$ and $M$ are tied at the two ends of the wire such that $m$ rests on the plane and $M$ hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of $100 \, m \, s^{-1}$. Choose the correct option for $m$ in $kg$.

State whether the following statements are True or False:
$(i)$ Compared to moist air,the speed of sound is greater in dry air.
$(ii)$ When the prongs of a tuning fork are rubbed,its frequency decreases.
$(iii)$ In the case of a stationary wave,the amplitudes of particles in any one loop are the same.
$(iv)$ In the case of a stationary wave,the amplitude of a particle decreases from node to antinode.

$A$ wave is travelling along a string. At an instant,the shape of the string is as shown in the figure. At this instant,point $A$ is moving upwards. Which of the following statements is/are correct?