Question

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

• A. $ \frac{\text{3}}{8} $
• B. $ \frac{2}{3} $
• C. $ \frac{8}{9} $
• D. $ \frac{9}{4} $

Answer 1

Answer: (D)

The frequency $ n=\frac{1}{2l}\sqrt{\frac{T}{m}} $ $ n\propto \frac{\sqrt{T}}{l} $ The ratio of tensions $ \frac{{{T}_{2}}}{{{T}_{1}}}={{\left( \frac{{{n}_{1}}}{{{n}_{1}}} \right)}^{2}}{{\left( \frac{{{l}_{2}}}{{{l}_{1}}} \right)}^{2}} $ $ ={{(2)}^{2}}\times {{\left( \frac{3}{4} \right)}^{2}} $ $ =\frac{9}{4} $