Two vibrating strings of the same material but length L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of the length L with frequency $v_{1}$ and the other with frequency$v2\ $. the ratio $v/v_{2}$is

Question

Dr. Abubacker · Accepted Answer

(d) Fundamental frequency,
$v = \frac{1}{2l}\sqrt{\frac{T}{m}} = \frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}ho}}\ $
$or\ \ \ \ v \propto \frac{1}{lr}$
$	herefore\ \frac{v_{1}}{v_{2}} = \frac{l_{2}r_{2}}{l_{1}r_{1}} = \frac{2L 	imes r}{L 	imes 2r} = 1$

Q. Two vibrating strings of the same material but length L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of the length L with frequency $v_{1}$ and the other with frequency$v2\ $. the ratio $v/v_{2}$is

Explanation

Reviewed by Dr. Abubacker

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