A string on a musical instrument is $50 cm$ long and its fundamental frequency is $270 Hz$. If the desired frequency of $1000 Hz$ is to be produced, the required length of the string is .... $cm$
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(a) $n \propto \frac{1}{l} \Rightarrow \frac{{{l_2}}}{{{l_1}}} = \frac{{{n_1}}}{{{n_2}}} $
$\Rightarrow {l_2} = {l_1}\left( {\frac{{{n_1}}}{{{n_2}}}} \right)$
$ = 50 \times \frac{{270}}{{1000}}$$ = 13.5\,cm$
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