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

A sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same, the length of the wire is doubled. Under what conditions would the tuning fork still be is resonance with the wire ?

A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9 kg$ is suspended from the wire. When this mass is replaced by a mass $M$, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of $M$ is … $kg$

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 $………..cm$.

The transverse displacement in a streched 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 $3.0 \times 10^{-2} \,kg$, then tension in string is ….. $N$