A tube $0.75 \mathrm{m}$ long is closed at one end. A stretched wire is placed near the open end. The wire is $0.25 \mathrm{m}$ long and has a mass of $0.01 \mathrm{kg}.$ It is held fixed at both ends and vibrates in its fundamental mode. It sets the air column in the tube into vibration at its fundamental frequency by resonance. If speed of sound is $330 \mathrm{m} {\mathrm{s}}^{-1}$ in air then tension in the wire is $11n \mathrm{N}.$ Value of $n,$ is

A source is oscillating between $A$ and $C$ with its position varying with time as $y=900 \cos \left(\frac{\pi t}{6}\right),$ where $y$ is in metre. An observer is situated at a distance $12 \mathrm{m}$ along the perpendicular bisector of $AC.$ Frequency emitted by source is $300 \mathrm{Hz}.$ Approximate frequency observed by observer when source is at $O$ is $5n \mathrm{Hz}.$ Value of $n,$ is [Velocity of sound in air $=300 \mathrm{m} {\mathrm{s}}^{-1}$]

A rod of mass $1.5 \mathrm{kg}$ and length $40 \mathrm{cm}$ is clamped with the help of two identical strings at the two ends as shown. A block of mass $5 \mathrm{kg}$ has to be connected on the rod. What should be the distance (in $\mathrm{cm}$ ) of point of suspension of block from the first end so that same tuning fork can vibrate the first string in second harmonic and the second string in third harmonic? $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$