A wire of density `9gm//cm^(3)` is stretched between two clamps 1.00m apart while subjected to an extension of 0.05cm. The lowest frequency of transverse vibration in the wire is (Assume Yong's modulus `Y=9xx10^(10)N//m^(2)`.

Explanation

` n = (1)/( 2l) sqrt(T//m)` for the lowest frequency . Here ` m = pi r^(2) rho`
`T ( tension ) = pi r^(2) xx ( gamma xx "strain") = pi r^(2) gamma epsilon`
` :. n = (I)/(2 I) sqrt (( pi r^(2) gamma epsilon)/( pi r^(2) rho))`
`= (1)/( 2 I) sqrt ( gamma epsilon)/(rho) = (1)/( 2 xx 1) sqrt(( 9 xx 10^(10) xx (0.05)/( 100))/( 9000)) = 35.4 Hz`