Uniform string of fundamental frequency of vibration f is divided into two segments by means of a bridge. If $f_{1} a n d f_{2}$ are fundamental frequencies of these segments then.

f_{1} f_{2} = f [f_{1} + f_{2}]

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2 f = f_{1} + f_{2}

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\sqrt{f} = {\sqrt{f}}_{1} + {\sqrt{f}}_{2}

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{\sqrt{f}}_{1} f_{2}

= 2 f

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Solution

The correct option is A $f_{1} f_{2} = f [f_{1} + f_{2}]$
Let the v be the speed of the wave

On string-

$f = \frac{v}{2 L}$

$f_{1} = \frac{v}{2 x}, f_{2} = \frac{v}{2 (L - x)}$

$\frac{1}{f_{2}} = \frac{2 L}{v} - \frac{2 x}{v}$

$\frac{1}{f_{2}} = \frac{1}{f} - \frac{1}{f_{1}}$

$\frac{1}{f_{2}} + \frac{1}{f_{1}} = \frac{1}{f}$

$\frac{1}{f} = \frac{f_{1} + f_{2}}{f_{1} f_{2}}$

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