Two wires made up of the same material are of equal length but their radii are in the ratio of 1:2. On stretching each of these two strings by the same tension, the ratio between the fundamental frequencies is

Question

Dr. Abubacker · Accepted Answer

(c) The fundamental frequency of a wire is given by
$v = \frac{1}{2l}\sqrt{\frac{T}{m}}$
Where $l$is length of wire, T the tension and m the mass per unit length.
$m = \frac{mass\ of\ wire}{length\ of\ wire}$
$= \frac{\pi r^{2}L 	imes density}{L} = \pi r^{2}d$
$v = \frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}d}}$
$\Longrightarrow \ \ v = \frac{1}{2rl}\sqrt{\frac{T}{\pi d}}\ $
$	herefore\frac{v_{1}}{v_{2}} = \frac{r_{2}}{r_{1}} = \frac{2}{1}$

Q. Two wires made up of the same material are of equal length but their radii are in the ratio of 1:2. On stretching each of these two strings by the same tension, the ratio between the fundamental frequencies is

Explanation

Reviewed by Dr. Abubacker

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