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

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, $\frac{r_{B}}{r_{A}} = 2$ is ( $r_{A}$ and $r_{B}$ are radii of the two the rods respectively)

TestHub · 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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