First slide

Standing waves

Question

Two vibrating strings of the same material but lengths L and 2 L have radii 2.r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length I with frequency n, and the other with frequency n₂. The ratio n₁, / n₂, is given by

Moderate

A

2
B

4
C

8
D

1

Solution

$n_{1} = \frac{1}{2 l} \sqrt{(\frac{T}{4 {πr}^{2} ρ})}) and n_{2} = \frac{1}{4 l} \sqrt{(\frac{T}{{πr}^{2} ρ})} ∴ \frac{n_{1}}{n_{2}} = 2 \times \frac{1}{2} = 1$

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