Question

If $n_{1}, n_{2}$ and $n_{3}$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by

• A. $\frac{1}{n}=\frac{1}{n_{1}}+\frac{1}{n_{2}}+\frac{1}{n_{3}}$
• B. $\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_{1}}}+\frac{1}{\sqrt{n_{2}}}+\frac{1}{\sqrt{n_{3}}}$
• C. $\sqrt{n}=\sqrt{n_{1}}+\sqrt{n_{2}}+\sqrt{n_{3}}$
• D. $n=n_{1}+n_{2}+n_{3}$

Answer 1

Answer: (A)

As $n \propto \frac{1}{l}$ or $l \propto \frac{1}{n}$
and $l =l_{1}+l_{2}+l_{3}$
$\Rightarrow \frac{1}{n}=\frac{1}{n_{1}}+\frac{1}{n_{2}}+\frac{1}{n_{3}}$