A wire of density `9000 kg//m^(3)` is stretched between two clamps `100 cm` apart while subjected to an extension od `0.05 cm`. What is the lowest frequency of transverse vibrations in the wire , assuming Young's modulus of the material to be `9 xx 10^(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`