A tuning fork produces $4$ beats per second when it is sounded with a stretched string having tension either $16$ or $9 \mathrm{kg} \mathrm{wt}.$ The frequency of the fork is $n \mathrm{Hz}.$ Value of $n\mathit{,}$ is

Two tuning forks with națural frequencies $170 \mathrm{Hz}$ each move relative to a stationary observer. One fork moves away from the observer while the other moves towards him at the same speed. The observer hears beats of frequency $2 \mathrm{Hz}.$ Speed of the tuning fork is $n \mathrm{m} {\mathrm{s}}^{-1}.$ Write the value of $n$ to the nearest ineteger.

(velocity of sound in air is $340 \mathrm{m} {\mathrm{s}}^{-1}$)

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? $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$