Question

The length of strings of a cello is $0.8m$. In order to change the pitch in frequency ratio $5/4$, their length should be decreased by

• A. $0.08m$
• B. $0.02m$
• C. $0.13m$
• D. $0.16m$

Answer 1

The correct option is D $0.16m$

Frequency $\nu \propto \frac{1}{l}$. So, $\frac{\nu }{{\nu }^{\prime }}=\frac{l^{\prime }}{l}$
$\Rightarrow 1-\frac{l^{\prime }}{l}=1-\frac{\nu }{{\nu }^{\prime }}=1-\frac{4}{5}=0.2$
$\Rightarrow \Delta l=0.2\times l=0.16m$