Transverse waves are generated in two steel wires A and B by attaching their free ends to a vibrating source of frequency 500Hz. 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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$1 : \sqrt{2}$

1:2

2:1

$\sqrt{2} : 1$

answer is D.

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Detailed Solution

We know velocity of a transverse wave in a stretched string is

$v = \sqrt{\frac{T}{ρA}}$

$\Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1} A_{2}}{T_{2} A_{1}}} = \sqrt{\frac{1 \times 4}{2 \times 1}} = \sqrt{2}$

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