1. Tardigrade
  2. Question
  3. Physics
  4. Two vibrating strings of same length, same cross section area and stretched to same tension is made of materials with densities ρ and 2 ρ. Each string is fixed at both ends. If v 1 represents the fundamental mode of vibration of the one made with density ρ and v2 for another, then v1 / v2 is:

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Two vibrating strings of same length, same cross section area and stretched to same tension is made of materials with densities $\rho$ and $2 \rho$. Each string is fixed at both ends. If $v _{1}$ represents the fundamental mode of vibration of the one made with density $\rho$ and $v_{2}$ for another, then $v_{1} / v_{2}$ is:

Waves

Solution:

Velocity of sound is inversely proportional to the square root of density of the medium.
i.e., $V \cdot \rho=$ constant
$\Rightarrow \frac{V_{1}}{V_{2}}=\sqrt{\frac{\rho_{2}}{\rho_{1}}}$
$=\sqrt{\frac{2 \rho}{\rho}}=\sqrt{2}$