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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 of that of B and tension in B is double that in A. What is the ratio of the velocities of waves in wires A and B?

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a

1 : 2

b

2 : 1

c

$1 : \sqrt{2}$

d

$\sqrt{2} : 1$

answer is D.

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Detailed Solution

$V = \sqrt{\frac{T}{m}} = \sqrt{\frac{T}{π r^{2} e}} V α \frac{\sqrt{T}}{D} \frac{V_{1}}{V_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} \times \frac{D_{2}}{D_{1}} = \sqrt{\frac{T}{2 T}} \times \frac{D}{\frac{D}{2}} = \frac{2}{\sqrt{2}} = \frac{\sqrt{2}}{1} = \sqrt{2} : 1$

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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 of that of B and tension in B is double that in A. What is the ratio of the velocities of waves in wires A and B?