$A$ 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:

Two uniform strings of mass per unit length $\mu$ and $4 \mu$,and length $L$ and $2 L$,respectively,are joined at point $O$,and tied at two fixed ends $P$ and $Q$,as shown in the figure. The strings are under a uniform tension $T$. If we define the frequency $v_0=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}$,which of the following statement$(s)$ is(are) correct?
$(A)$ With a node at $O$,the minimum frequency of vibration of the composite string is $v_0$
$(B)$ With an antinode at $O$,the minimum frequency of vibration of the composite string is $2 v_0$
$(C)$ When the composite string vibrates at the minimum frequency with a node at $O$,it has $6$ nodes,including the end nodes
$(D)$ No vibrational mode with an antinode at $O$ is possible for the composite string

The wavelength of light in the visible part $(\lambda_V)$ and for sound $(\lambda_S)$ are related as:

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?

$A$ 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 = $320 \text{ m/s}$)

Fill in the blanks:
$(i)$ If the fundamental frequency of a given closed pipe is $50 \ Hz$,then the frequency for the second overtone is ...... .
$(ii)$ The speed of sound in air at $STP$ is ...... .
$(iii)$ In the case of sound waves,in order to experience beats quite clearly,the value of the beat frequency $|f_1 - f_2|$ should not be greater than ...... .