$A$ second harmonic has to be generated in a string of length $l$ stretched between two rigid supports. The points where the string has to be plucked and touched are

$A$ 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

$A$ string on a musical instrument is $50 \ cm$ long and its fundamental frequency is $270 \ Hz$. If the desired frequency of $1000 \ Hz$ is to be produced,the required length of the string is .... $cm$.

The tension in a piano wire is $10 \ N$. What should be the tension in the wire to produce a note of double the frequency (in $N$)?

$A$ stretched string resonates with a tuning fork of frequency $512 \; Hz$ when the length of the string is $0.5 \; m$. The length of the string required to vibrate resonantly with a tuning fork of frequency $256 \; Hz$ would be .......... $m$.

$A$ segment of wire vibrates with a fundamental frequency of $450 \,Hz$ under a tension of $9 \,kg-wt$. The tension at which the fundamental frequency of the same wire becomes $900 \,Hz$ is: