Two vibrating strings of same length, same cross section area and stretched to same tension is made of materials with densities $\mathrm{\rho }$ and 2$\mathrm{\rho }$.Each string is fixed at both ends. If ${\mathrm{v}}_1$ represents the fundamental mode of vibration of the one made with density $\mathrm{\rho }$ and ${\mathrm{v}}_2$ for another, then $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}$ is:

• A

  $\frac{1}{2}$

• B

  2

• C

  $\sqrt{2}$

• D

  $\frac{1}{\sqrt{2}}$