Question

In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to $\frac{3}{4}$th of the original length and the tension is changed. The factor by which the tension is to be changed, is

• A. 3/8
• B. 2/3
• C. 8/9
• D. 9/4

Answer 1

The correct option is D 9/4

$n=\frac{1}{2l}\sqrt{\frac{T}{m}}\Rightarrow n\propto \frac{\sqrt{T}}{l}$

$\Rightarrow \frac{T_2}{T_1}={\left(\frac{n_2}{n_1}\right)}^2{\left(\frac{l_2}{l_1}\right)}^2=(2{)}^2{\left(\frac{3}{4}\right)}^2=\frac{9}{4}$