A steel wire of length lm, mass 0.1 kg and uniform cross-sectional area `10^(-6)m^(2)` is rigidly fixed at both ends. The temperature of the wire is lowered by `20^(0)C`. If the transverse waves are set up by plucking the string in the middle, calculate the frequency of the fundamental mode of vibration `[Y=2xx10^(11)N//m^(2) and alpha=1.21xx10^(-5)l^(0)C]`

Explanation

`f=(1)/(2L) sqrt((Y A alpha Delta theta)/(mu))`
Substituting the given values
`Y=(1)/(2xx1) sqrt((2xx10^(11)xx10^(-6)xx1.21xx10^(-5)xx20)/((0.1//1))=11Hz`