$A$ 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 upward. Then:
$(a)$ The wave is travelling to the left.
$(b)$ At this instant,$C$ is moving downward.
$(c)$ The amplitude of the wave is greater than the displacement of point $B$ at this instant.
$(d)$ The phase at $A$ is less than the phase at $C$.
Select the correct statements:

Explain why (or how):
$(a)$ in a sound wave,a displacement node is a pressure antinode and vice versa,
$(b)$ bats can ascertain distances,directions,nature,and sizes of the obstacles without any eyes,
$(c)$ a violin note and sitar note may have the same frequency,yet we can distinguish between the two notes,
$(d)$ solids can support both longitudinal and transverse waves,but only longitudinal waves can propagate in gases,and
$(e)$ the shape of a pulse gets distorted during propagation in a dispersive medium.

In Quincke's tube,a detector detects minimum intensity. Now,one of the tubes is displaced by $5 \, cm$. During displacement,the detector detects maximum intensity $10$ times,and finally a minimum intensity (when displacement is complete). The wavelength of sound is .... $cm$.

$A$ 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 $kg$.

$A$ pipe open at one end has a length of $0.8 \text{ m}$. At the open end of the tube, a string $0.5 \text{ m}$ long is vibrating in its first overtone and resonates with the fundamental frequency of the pipe. If the tension in the string is $50 \text{ N}$, what is the mass of the string (in $\text{ g}$)? (Neglect end correction, Speed of sound = $320 \text{ m/s}$)

An object of density $2000 \ kg \ m^{-3}$ is hung from a thin light wire. The fundamental frequency of the transverse waves in the wire is $200 \ Hz$. If the object is immersed in water such that half of its volume is submerged,then the fundamental frequency of the transverse waves in the wire is (in $Hz$)