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?

When the tense wire of a sitar is pulled slightly from the middle and then released,which type of waves are produced?

The frequency of a stretched uniform wire under tension is in resonance with the fundamental frequency of a closed tube. If the tension in the wire is increased by $8 \ N$,it is in resonance with the first overtone of the closed tube. The initial tension in the wire is .... $N$.

Match Column-$1$ with Column-$2$.

Column-$1$	Column-$2$
$(a)$ Light waves	$(i)$ Mechanical and transverse.
$(b)$ Sound waves	$(ii)$ Mechanical and longitudinal.
$(c)$ Earthquake waves	$(iii)$ Non-mechanical and transverse.
$(d)$ Waves on a tense string	$(iv)$ Mechanical,transverse and longitudinal.

$A$ man standing in front of a mountain beats a drum at regular intervals. The rate of drumming is gradually increased and he finds that the echo is not heard distinctly when the rate becomes $40$ per minute. He then moves nearer to the mountain by $90 \ m$ and finds that the echo is again not heard when the drumming rate becomes $60$ per minute. The distance between the mountain and the initial position of the man is .... $m$

Two tuning forks $A$ and $B$ give $5$ beats per second. Fork $A$ resonates with a closed air column $20 \ cm$ long and fork $B$ with an open air column $40.5 \ cm$ long. Neglecting end correction,the frequencies of tuning forks $A$ and $B$ are respectively.