$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions right-angled to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at the point $D$ where a detector is placed. The maximum intensity produced at $D$ is given by

$A$ 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:

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

At a certain moment, the photograph of a string on which a harmonic wave is travelling to the right is shown. Then, which of the following is true regarding the velocities of the points $P$, $Q$ and $R$ on the string?

$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions at a right angle to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at the point $D$ where a detector is placed. If a minimum is formed at the detector,then the magnitude of the wavelength $\lambda$ of the wave produced is given by:

In the Kundt's tube experiment (shown in fig. $(i)$),the rod is clamped at the center. In the modified experiment (shown in fig. $(ii)$),the rod is clamped at the end. It is known that the speed of sound in air is $330\ m/s$,the powder piles up at successive distances of $0.6\ m$,and the length of the rod used is $1\ m$. Calculate the speed of sound in the rod in $m/s$.