The length of a sonometer wire tuned to a frequency of $250 \ Hz$ is $0.60 \ m$. The frequency of the tuning fork with which the vibrating wire will be in tune when the length is made $0.40 \ m$ is .... $Hz$.

$A$ stretched string is divided into three segments of lengths $50\,cm$,$40\,cm$,and $10\,cm$ with the help of bridges. Their vibrations will have frequencies in the ratio:

$A$ tuning fork vibrating with a sonometer having a wire of length $20 \,cm$ produces $5$ beats per second. The beat frequency does not change if the length of the wire is changed to $21 \,cm$. The frequency of the tuning fork must be ............ $Hz$.

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 $N$)?

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

The fundamental frequency of a sonometer wire is $n$. If the length and diameter of the wire are doubled while keeping the tension constant,what is the new fundamental frequency?