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Two string of same material are stretche...

Two string of same material are stretched to same tension between rigid supports. If diameter of second wire is double than that of first wire and fundamental frequency of first is equal to third harmonic of second wire, find ratio of their lengths.

Text Solution

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`f_(0) =(1)/(2L) sqrt((T)/(pxx(pi(d^(2))/(4)))) = (1)/(L) sqrt((T)/(rhopi))`
`(f_(0))_(1st) = 3(f_(0))_(2nd)`
`rArr (1)/(L_(1)d_(1)) = (3)/(L_(3)d_(2)) rArr (L_(1))/(L(2)) = (d_(2))/(3d_(1)) = (2)/(3)`
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