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Question

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 vA and on B with speed vB. The ratio vA/vB is

A
1/2
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B
2
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C
1/4
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D
4
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Solution

The correct option is B 1/2
Velocity of a transverse wave in a stretched string v=Tμ
where T is the tension of the string and μ is mass per unit length of the string.
μ=πr2×ρ
where r is the radius or the string and ρ is the density of the material of the string.
v=1rTπρ
Since T,ρ are constant
v1r
vAvB=rBrA=(rB2rB)=12.

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