First slide

Standing waves

Question

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

Moderate

A

2 : 3
B

2 : 4
C

2 : 5
D

2 : 6

Solution

$v = \frac{1}{l (3 D)} \sqrt{\frac{2 T}{πρ}}; v^{'} = \frac{1}{lD} \sqrt{\frac{T}{π (2 ρ)}}$
$\frac{v}{v^{'}} = \frac{\sqrt{2}}{3} \times \sqrt{2} = \frac{2}{3}$

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