Question:
If the ratio of the Young's moduli and densities of two rods of different materials are respectively, \(3:2\) and \(3:1\), then the ratio of the velocities of sound in the rods is
If the ratio of the Young's moduli and densities of two rods of different materials are respectively, \(3:2\) and \(3:1\), then the ratio of the velocities of sound in the rods is
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\(v = \sqrt{\frac{Y}{\rho}}\) for sound in solids. Ratio = \(\sqrt{\frac{Y_1/Y_2}{\rho_1/\rho_2}}\).
Updated On: Apr 24, 2026
- \(1:2\)
- \(2:1\)
- \(\sqrt{2}:1\)
- \(1:\sqrt{2}\)
- \(1:3\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Velocity of sound in a rod: \(v = \sqrt{\frac{Y}{\rho}}\), where \(Y\) = Young's modulus, \(\rho\) = density.
Step 2: Detailed Explanation:
\(\frac{v_1}{v_2} = \sqrt{\frac{Y_1/Y_2}{\rho_1/\rho_2}} = \sqrt{\frac{3/2}{3/1}} = \sqrt{\frac{3}{2} \times \frac{1}{3}} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}\)
Ratio \(v_1 : v_2 = 1 : \sqrt{2}\)
Step 3: Final Answer:
The ratio is \(1:\sqrt{2}\).
Velocity of sound in a rod: \(v = \sqrt{\frac{Y}{\rho}}\), where \(Y\) = Young's modulus, \(\rho\) = density.
Step 2: Detailed Explanation:
\(\frac{v_1}{v_2} = \sqrt{\frac{Y_1/Y_2}{\rho_1/\rho_2}} = \sqrt{\frac{3/2}{3/1}} = \sqrt{\frac{3}{2} \times \frac{1}{3}} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}\)
Ratio \(v_1 : v_2 = 1 : \sqrt{2}\)
Step 3: Final Answer:
The ratio is \(1:\sqrt{2}\).
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