Question

A string has tension $T$. For tripling the frequency, the tension in string will become

• A. $3T$
• B. $\frac{T}{9}$
• C. $\frac{T}{\sqrt 3}$
• D. $9T$

Answer 1

Answer: (D)

$9T$

Answer 2

The frequency of a string
$f=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}$
where $\mu$ is mass per unit length of strings and $T$ is tension in the string.
$\therefore f \propto \sqrt{T} \Rightarrow T \propto f^{2}$
$\Rightarrow \frac{T_{1}}{T_{1}}=\left(\frac{f_{2}}{f_{1}}\right)^{2}$
Given, $f_{1}=f, f_{2}=3 f$ and $T_{1}=T$
$\therefore \frac{T_{2}}{T}=\left(\frac{3 f}{f}\right)^{2}$
$\Rightarrow T_{2}=9 T$