When a string is divided into three segments of length $l_1, l_2 and l_3$ the fundamental frequencies of these three segments are ${\mathrm{f}}_1 , {\mathrm{f}}_{2 } \mathrm{and} {\mathrm{f}}_3$ respectively. The original fundamental frequency (f) of the string is

• A

  $\frac{1}{\sqrt{\mathrm{f}}} = \frac{1}{\sqrt{{\mathrm{f}}_1}}+\frac{1}{\sqrt{{\mathrm{f}}_2}}+\frac{1}{\sqrt{{\mathrm{f}}_3}}$

• B

  $\sqrt{\mathrm{f}} = \sqrt{{\mathrm{f}}_1}+\sqrt{{\mathrm{f}}_2}+\sqrt{{\mathrm{f}}_3}$

• C

  $\mathrm{f} = {\mathrm{f}}_1+{\mathrm{f}}_2 + {\mathrm{f}}_3$

• D

  $\frac{1}{\mathrm{f}} = \frac{1}{{\mathrm{f}}_1}+\frac{1}{{\mathrm{f}}_2}+\frac{1}{{\mathrm{f}}_3}$