When a sonometer wire vibrates in the third overtone,there are:

$A$ tuning fork gives $4$ beats with $50 \, cm$ length of a sonometer wire. If the length of the wire is shortened by $1 \, cm$,the number of beats remains the same. The frequency of the fork is ............. $Hz$.

To increase the frequency of a stretched string from $100 \ Hz$ to $400 \ Hz$,the tension in the string has to be changed by how many times?

If $n_{1}, n_{2}$ and $n_{3}$ are the fundamental frequencies of three segments into which a string is divided,then the original fundamental frequency $n$ of the string is given by

In an experiment with a sonometer,when a mass of $180\,g$ is attached to the string,it vibrates with a fundamental frequency of $30\,Hz$. When a mass $m$ is attached,the string vibrates with a fundamental frequency of $50\,Hz$. The value of $m$ is $.........\,g$.

When the tension in a string is increased by $3 \ kg \ wt$,the frequency of the fundamental mode increases in the ratio $2:3$. The initial tension in the string is: (in $kg \ wt$)