Question

If Young's modulus and densities are in the ratio 3:2 and 3:1 respectively, the ratio of velocity of sound is:

• A. \( 3:1 \)
• B. \( 3:2 \)
• C. \( 1:3 \)
• D. \( 1:2 \)

Hint:

When comparing the velocities of sound in two materials, remember that the velocity depends on the square root of the ratio of Young's modulus to density.

Answer 1

The Correct Option is A

The velocity of sound in a material is given by: \[ v = \sqrt{\frac{Y}{\rho}} \] Where: - \( Y \) is the Young's modulus, - \( \rho \) is the density. We are given the ratios: \[ \frac{Y_1}{Y_2} = \frac{3}{2}, \quad \frac{\rho_1}{\rho_2} = \frac{3}{1} \] The ratio of the velocities of sound is: \[ \frac{v_1}{v_2} = \sqrt{\frac{Y_1/\rho_1}{Y_2/\rho_2}} = \sqrt{\frac{Y_1}{Y_2} \times \frac{\rho_2}{\rho_1}} = \sqrt{\frac{3/2}{3/1}} = \sqrt{\frac{1}{2}} = \frac{3}{1} \]
Thus, the ratio of the velocity of sound is \( 3:1 \).