The system of two rods shown in figure is vibrating at the same frequency having standing wave with junction as node a standing wave. The ratio of the number of antinodes in the two rods, if the radii of the rods are in the ratio, r B r A = 2 is ( r A and r B are radii of the two the rods respectively)

Question

The system of two rods shown in figure is vibrating at the same frequency having standing wave with junction as node a standing wave. The ratio of the number of antinodes in the two rods, if the radii of the rods are in the ratio, r B r A = 2 is ( r A and r B are radii of the two the rods respectively), 1, 2, 3, 4

MARKS App · Accepted Answer

For rod A , f 1 = n 1 2 l T ρ A 1 For rod B , f 2 = n 2 2 l T ρ A 2 Given f 1 = f 2 . n 1 2 l T ρ A 1 = n 2 2 l T ρ A 2 ∵ r B = 2 r A , A 2 = 4 A 1 n 1 2 l T ρ A 1 = n 2 2 l T ρ ( 4 A 1 ) n 1 = n 2 2 n 2 n 1 = 2

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