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When a string is divided into three segments of length l_{1}, l_{2} and l_{3}, the fundamental frequencies of these three segments are \nu_{1 }, \nu_{2} and \nu_{3} respectively. The original fundamental frequency (\nu) of the string is:

Option: 1

\sqrt{\nu} = \sqrt{\nu_{1 }} + \sqrt{\nu_{2}} + \sqrt{\nu_{3}}


Option: 2

\nu = \nu_{1} + \nu_{2} + \nu_{3}


Option: 3

\frac{1}{\nu} = \frac{1}{\nu_{1}} + \frac{1}{\nu_{2}} + \frac{1}{\nu_{3}}


Option: 4

None of these


Answers (1)

best_answer

Fundamental frequency,

        \nu = \frac{1}{2l} \sqrt{\frac{T}{\nu}}

\implies v \alpha \frac{1}{l}

           v = \frac{k}{l}

\therefore l_1 = \frac{k}{v1}        \therefore l_2 = \frac{k}{v2}        \therefore l_3 = \frac{k}{v3}

\therefore \frac{1}{\nu} = \frac{1}{\nu_{1}} + \frac{1}{\nu_{2}} + \frac{1}{\nu_{3}}

Posted by

Gautam harsolia

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