If ${n_1},{n_2},{n_3}.........$ are the frequencies of segments of a stretched string, the frequency $n$ of the string is given by
Medium
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(c) For a vibrating string
${n_1}{l_1} = {n_2}{l_2} = {n_3}{l_3}..... = $constant $= k$ (say) $= nl$
Also ${l_1} + {l_2} + {l_3} + {l_4} + ...... = 1$
$\frac{k}{{{n_1}}} + \frac{k}{{{n_2}}} + \frac{k}{{{n_3}}} + \frac{k}{{{n_4}}} + .... = \frac{k}{n}$==> $\frac{1}{n} = \frac{1}{{{n_1}}} + \frac{1}{{{n_2}}} + \frac{1}{{{n_3}}} + .......$
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