The tension of a stretched string is increased by $69\%$. In order to keep its frequency of vibration constant, its length must be increased by .... $\%$
A$20$
B$30$
C$\sqrt {69}$
D$69$
Medium
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B$30$
b (b)$n \propto \frac{{\sqrt T }}{l}$$ \Rightarrow l \propto \sqrt T $(As $n$= constant)
==>$\frac{{{l_2}}}{{{l_1}}} = \sqrt {\frac{{{T_2}}}{{{T_1}}}} = {l_1}\sqrt {\frac{{169}}{{100}}} \Rightarrow {l_2} = 1.3{l_1} = {l_1} + 30\% $ of ${l_1}$
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