String of length $l$ is divided into three segments of lengths $l_{1}, l_{2}$ and $l_{3}$ with the f

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String of length $l$ is divided into three segments of lengths $l_{1}, l_{2}$ and $l_{3}$ with the fundamental frequencies $n_{1}, n_{2}$ and $n_{3}$ respectively. The original fundamental frequency of the string $n$ is given by\

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(b): The fundamental frequency of a string is inversely proportional to its length. \ $ n \propto \frac{1}{l} $ \ Length of the original string, $L=l_{1}+l_{2}+l_{3}$ \Since $n \propto \frac{1}{l}$\ $	herefore l=\frac{K}{n}, l_{1}=\frac{K}{n_{1}}, l_{2}=\frac{K}{n_{2}}$ and $l_{3}=\frac{K}{n_{3}}$\ where $K$ is a constant.\ From eq. (i), we get \ $ \frac{K}{n}=\frac{K}{n_{1}}+\frac{K}{n_{2}}+\frac{K}{n_{3}} 	ext { or } \frac{1}{n}=\frac{1}{n_{1}}+\frac{1}{n_{2}}+\frac{1}{n_{3}} $