Question

If $n_1,n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the fundamental frequency n of the original string is given by

• A. $n=n_1+n_2+n_3$
• B. $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$
• C. $\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}$
• D. $\sqrt{n}=\sqrt{n_1}+\sqrt{n_2}+\sqrt{n_3}$

Answer 1

The correct option is B

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

$L=L_1+L_2+L_3$ and $n\propto \frac{1}{L}$ for a string of length in fundamental mode of vibration,
So, $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$