Question

2 strings x and y of the same material same length have a frequency as 450Hz and 200 Hz. Find the ratio of their tension (Tx:Ty).

Answer 1

The frequency of a string is given by,

$\sf{\longrightarrow \nu=\dfrac{1}{2L}\sqrt{\dfrac{T}{\mu}}}$

In case of strings of same material and length,

$\sf{\longrightarrow \nu\propto\sqrt T}$

$\sf{\longrightarrow T\propto \nu^2}$

According to the question, ratio of frequencies of the string is,

$\sf{\longrightarrow \dfrac{\nu_x}{\nu_y}=\dfrac{450}{200}}$

$\sf{\longrightarrow \dfrac{\nu_x}{\nu_y}=\dfrac{9}{4}}$

Therefore, ratio of their tensions is,

$\sf{\longrightarrow \dfrac{T_x}{T_y}=\left(\dfrac{\nu_x}{\nu_y}\right)^2}$

$\sf{\longrightarrow\underline{\underline{\dfrac{T_x}{T_y}=\dfrac{81}{16}}}}$