Transverse waves are generated in two uniform wires A and B of the same material by attaching their free ends to a vibrating source of frequency 200 Hz. The area of cross section of A is half that of B while tension on A is twice than on B. The ratio of wavelengths of the transverse waves in A and B is

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$1: \sqrt{2}$

2 : 1

1 : 2

$\sqrt{2} : 1$

answer is D.

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Detailed Solution

$λ = \sqrt{\frac{T}{A}} \frac{λ_{1}}{λ_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} \sqrt{\frac{A_{2}}{A_{1}}} = \sqrt{\frac{2 T}{T}} \sqrt{\frac{2 A}{A}} = \frac{2}{1}$

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