A steel wire of length `1 m` and mass `0.1 kg` and having a uniform cross-sectional area of `10^(-6) m^(2)` is rigidly fixed at both ends. The temperature of the wire is lowered by `20^(@)C`. If the wire is vibrating in fundamental mode, find the frequency (in Hz). `(Y_(steel)=2xx 10^(11) N//m^(2),alpha_(steel)=1.21 xx 10^(-5)//.^(@)C)`.

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`