Speed of a transverse wave on a straight wire (mass $6.0\; g$,length $60\; cm$,and area of cross-section $1.0\; mm^{2}$) is $90\; ms^{-1}$. If the Young's modulus of the wire is $16 \times 10^{11}\; Nm^{-2}$,the extension of the wire over its natural length is: (in $; mm$)

Diffraction of sound waves is more evident than light waves in daily life because:

$A$ 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 $N$)

$A$ massless rod of length $L$ 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 in $AB$ is equal to the $2^{nd}$ harmonic frequency in $CD$. The value of $x$ is

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 $m/s$.