A steel wire is rigidly fixed at both ends its length mass and cross sectional area are 1m, 0.1 kg and `10^(6)m^(2)` respectively then the temperature of the wire is lowered by `20^(@)C` if the transverse waves are setup by plucking the wire at 0.25m from one end and assuming that wire vibrates with minimum number of loops possible for such a case. Find the frequency of vibration (in Hz). [coefficient of linear expansion of steel `=1.21xx10^(-6)//.^(@)C` and young's modulus `=2xx10^(11)//N//m^(2)`]

Explanation

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`DeltaL=L alpha DeltaT`
for the condition minimum 2 loops will be formed
`:. F=2 f+(0),f=(2)/(2L)sqrt((YAalphaDeltaT)/((M)/(L)))=sqrt((YA alphaDeltaT)/(ML)`