When a string is divided into three segments of lengths ${\mathit{\text{l}}}_1$, ${\mathit{\text{l}}}_2$ and ${\mathit{\text{l}}}_3$ the fundamental frequencies of these three segments are ${\mathrm{\nu }}_1$, ${\mathrm{\nu }}_2$ and ${\mathrm{\nu }}_3$ respectively. The original fundamental frequency $\left(\mathrm{\nu }\right)$ of the string is

• A

  $\sqrt{\mathrm{\nu }}=\sqrt{{\mathrm{\nu }}_1}+\sqrt{{\mathrm{\nu }}_2}+\sqrt{{\mathrm{\nu }}_3}$
• B

  $\mathrm{\nu }={\mathrm{\nu }}_1+{\mathrm{\nu }}_2+{\mathrm{\nu }}_3$
• Correct answer
  C

  $\frac{1}{\mathrm{\nu }}=\frac{1}{{\mathrm{\nu }}_1}+\frac{1}{{\mathrm{\nu }}_2}+\frac{1}{{\mathrm{\nu }}_3}$
• D

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

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