A steel wire of length 1 m, mass 0.1 kg and uniform cross-sectional area `10^(-6)m^(2)` is rigidly fixed at both ends. The temperature of wire is lowered by 20°C. If transverse waves are set up by plucking the string in the middle, calculate the frequency (In S.I. units) of the fundamental mode of vibration. Young’s modulus of steel `=2xx10^(11)N//m^(2)`, coefficient of linear expansion of steel`=1.21xx10^(-6)(degC)^(-1)`.

Answer

11 Hz

Explanation

For wire, `DeltaL=L alpha theta = (FL)/(AY)rArr D=AY alpha theta`
`:. f=(1)/(2L)sqrt((F)/(mu))=(1)/(2xx1)sqrt((10^(-6)xx2xx10^(11)xx1.21 xx10^(5)xx20)/(0.1))`
`=11Hz`