The fundamental frequency of a sonometer wire increases by $20\text{Hz}$ if its tension is increased by $44\%$ . The fundamental frequency of the sonometer wire is $\text{Hz}$ is

Given ,

Frequency $n_1=n$

Frequency $n_2=n+20$

Tension $T_1=100$

Tension $T_2=144$

$\frac{n_2}{n_1}=\sqrt{\frac{T_2}{T_1}}$

$\frac{n+20}{n}=\sqrt{\frac{T_2}{T_1}}$

$\frac{n+20}{n}=\sqrt{\frac{144}{100}}=\frac{12}{10}$

$10n+200=12n$

$2n=200$

$\therefore n=100\text{Hz}$