Q.

Two wires are kept tight between the same pair of supports. The tensions in the wires are in the ratio 2 : 1, the radii are in the ratio 3: 1 and the densities are in the ratio 1: 2. The ratio of their fundamental frequencies is

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a

2 : 3

b

2 : 4

c

2 : 5

d

2 : 6

answer is A.

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Detailed Solution

v = 1l(3D)2Tπρ;   v' = 1lDTπ(2ρ)vv' = 23×2 = 23
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Two wires are kept tight between the same pair of supports. The tensions in the wires are in the ratio 2 : 1, the radii are in the ratio 3: 1 and the densities are in the ratio 1: 2. The ratio of their fundamental frequencies is