Question

A stretched wire of some length under a tension is vibrating with its fundamental frequency. Its length is decreased by $45\%$ and tension is
increased by $21\%$. Now its fundamental frequency:

• A. increases by $50\%$
• B. increases by $100\%$
• C. decreases by $50\%$
• D. decreases by $25\%$

Answer 1

The correct option is B increases by $100\%$

length is decreased by $45\%$ $\Rightarrow l^{{}^{\prime }}=\frac{55l}{100}$
Tension is increased by $21\%$ $\Rightarrow T^{{}^{\prime }}=\frac{121T}{100}$
$f=\frac{l}{2l}\sqrt{\frac{T}{\mu }}$
$\frac{f_1}{f_2}=\frac{55}{100}\times \frac{100}{11}$
$\frac{f_1}{f_2}=\frac{1}{2}$
$f_2=2f_1$
$f$ is increased $100\%$