$A$ guitar string of length $90\,cm$ vibrates with a fundamental frequency of $120\,Hz.$ The length of the string producing a fundamental frequency of $180\,Hz$ will be $...........cm$.

In a Sonometer experiment,the frequency of the tuning fork used is $288 \ Hz$. Harmonics will '$NOT$' be produced at the frequency: (in $Hz$)

$A$ uniform wire of length $L$,diameter $D$,and density $\rho$ is stretched by a tension $T$. The frequency $f$ of the wire is proportional to:

$A$ tuning fork produces $4$ beats per second when sounded with a sonometer wire of vibrating length $48 \ cm$. It also produces $4$ beats per second when the vibrating length is $50 \ cm$,keeping the tension in the wire the same. What is the frequency of the tuning fork in $Hz$?

The transverse displacement in a stretched string is given by $y = 0.06 \sin \left( \frac{2\pi}{3}x \right) \cos (120\pi t)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The length of the string is $1.5 \, m$ and its mass is $3.0 \times 10^{-2} \, kg$. The tension in the string is ..... $N$.

The fundamental frequency of a sonometer wire is $n$. If its radius is doubled and its tension becomes half,while the material of the wire remains the same,the new fundamental frequency will be