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 $v_{1}, v_{2}$ and $v_{3}$ respectively. The original fundamental frequency (v) of the string is

• A

  $\quad \sqrt{v}=\sqrt{v_{1}}+\sqrt{v_{2}}+\sqrt{v_{3}}$
• B

  $v=v_{1}+v_{2}+v_{3}$
• Correct answer
  C

  $\frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}+\frac{1}{v_{3}}$.
• D

  $\frac{1}{\sqrt{v}}=\frac{1}{\sqrt{v_{1}}}+\frac{1}{\sqrt{v_{2}}}+\frac{1}{\sqrt{v_{3}}}$

Hence, the correct answer is option: 'C'.