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When two organ pipes with fundamental frequencies n_(1)and n_(2) are connected in series, what will be the resultant fundamental frequency?

Answer» <html><body><p>`(n _(1) + n_(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>))`<br/>`(n _(2) + n _(2))/( 2)`<br/>`sqrt (n_(1) n _(2) + n _(2) ^(2))`<br/>`(n _(2)n _(2))/( n _(1) + n _(2))` </p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :We have `f = f _(<a href="https://interviewquestions.tuteehub.com/tag/min-548008" style="font-weight:bold;" target="_blank" title="Click to know more about MIN">MIN</a>) = (v)/(2L)` <br/> For open pipe `<a href="https://interviewquestions.tuteehub.com/tag/implies-1037962" style="font-weight:bold;" target="_blank" title="Click to know more about IMPLIES">IMPLIES</a> L =(v)/(2f)` <br/> (i)For first pipe. `f _(1) = (v )/( 2L _(1)) = L _(1) = (v)/( 2f _(1))` <br/> (ii) For second pipe, `f _(2) = (v)/( 2L _(2)) implies L _(2) = (v )/(2f _(2))` <br/> Here,` L = L _(1) + L _(2)` <br/> `therefore (v )/( 2f)= (v)/( 2f _(1)) + (v)/( 2f _(2))` <br/> `therefore (1)/(f) = (1)/(f _(1)) + (1)/(f _(2))` <br/> As per the <a href="https://interviewquestions.tuteehub.com/tag/notations-1125257" style="font-weight:bold;" target="_blank" title="Click to know more about NOTATIONS">NOTATIONS</a> used in the equation.<br/> `n = (n _(1) n _(2))/( n _(1) +n_(2))`</body></html>


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