If {n_1}, {n_2}, {n_3}, dots are the frequenc | vedclass

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(C) For a vibrating string,the product of frequency $n$ and length $l$ is constant,i.e.,$n_1 l_1 = n_2 l_2 = n_3 l_3 = \dots = nl = k$ (constant).Sinc

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$\frac{1}{n} = \frac{1}{{{n_1}}} + \frac{1}{{{n_2}}} + \frac{1}{{{n_3}}} + \dots$

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(C) For a vibrating string,the product of frequency $n$ and length $l$ is constant,i.e.,$n_1 l_1 = n_2 l_2 = n_3 l_3 = \dots = nl = k$ (constant).Since the total length of the string is the sum of the lengths of its segments,we have $l_1 + l_2 + l_3 + \dots = l$.Substituting $l_i = \frac{k}{n_i}$ and $l = \frac{k}{n}$ into the equation,we get $\frac{k}{n_1} + \frac{k}{n_2} + \frac{k}{n_3} + \dots = \frac{k}{n}$.Dividing both sides by $k$,we obtain $\frac{1}{n} = \frac{1}{n_1} + \frac{1}{n_2} + \frac{1}{n_3} + \dots$.

If ${n_1}, {n_2}, {n_3}, \dots$ are the frequencies of segments of a stretched string,the frequency $n$ of the string is given by

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