Transverse waves are generated in two steel wires A and B by attaching their free ends to a vibrating source of frequency 500 Hz. The diameter of A is half that of B and tension on B is double that on A. What is the ratio of the velocities of waves in wires A and B?

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2 : 1

$\sqrt{2}$ : 1

1 : $\sqrt{2}$

1 : 2

answer is D.

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Detailed Solution

Diameter $D_{A} = \frac{1}{2} D_{B} T_{B} = 2 T_{A}$
$V \propto \frac{\sqrt{T}}{r} \propto \frac{\sqrt{T}}{D}; \frac{V_{A}}{V_{B}} = \sqrt{\frac{T_{A}}{T_{B}} x \frac{D_{B}}{D_{A}}} = \sqrt{\frac{1}{2} x 2} = \sqrt{2} : 1$

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