The frequency of the first harmonic of a string stretched between two points is $100 \, Hz$. The frequency of the third overtone is ... $Hz$.

$A$ 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

$A$ string in a musical instrument is $50 \ cm$ long and its fundamental frequency is $800 \ Hz$. If a frequency of $1000 \ Hz$ is to be produced,then the required length of the string is ..... $cm$.

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?

The fundamental frequency of a sonometer wire is $50 \ Hz$ for a given length and tension. If the length is increased by $25 \%$ while keeping the tension constant,what is the percentage change in the frequency of the second harmonic?

$A$ string vibrates in its fundamental mode when a tension $T_1$ is applied to it. If the length of the string is decreased by $25 \%$ and the tension applied is changed to $T_2$,the fundamental frequency of the string increases by $100 \%$,then $\frac{T_2}{T_1} =$ (Linear density of the string is constant)