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Two strings A and B made of same materia...

Two strings A and B made of same material are stretched by same tension. The radius of string A is double of the radius of B. A transverse wave travels on A with speed `v_A` and on B with speed `v_B`. The ratio `v_A/v_B` is

A

`1/4`

B

`1/2`

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
`v_(A) = sqrt(T/m) :. v_(A)/v_(B) = sqrt((m_(B))/(m_(A))) ` ....(1)
But m = mass per unit length ` = v xx d = pir^(2) `
`:. sqrt((m_(B))/(m_(A))) = sqrt((pi r_(2)^(2)d)/(pi r_(1)^(2)d)) = (r_(2)/(2r_(2))) = 1/2 `
` :. " from " (1) , v_(A)/v_(B) = sqrt((m_(B))/(m_(A))) = 1/2 `
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