A steel wire of length `1m`, mass `0.1kg` and uniform cross-sectional area `10^(-6)m^(2)` is rigidly fixed at both ends. The temperature of the wire is lowered by `20^(@)C`. If transverse waves are set up by plucking the string in the middle.Calculate the frequency of the fundamental mode of vibration.
Given for steel `Y = 2 xx 10^(11)N//m^(2)`
`alpha = 1.21 xx 10^(-5) per ^(@)C`

Answer

11

Explanation

Frequency of the wire in fundamental mode `f_0=(1)/(2l)sqrt((T)/(mu))`
When the temperature of wire is changed the tension developed `T=YAprop(triangletheta)` and mass per init length `mu=Arho`
`therefore f_0=1/(2l)sqrt(((YAproptriangletheta)/(M)))`
Here we are given `l=1m,y=2xx10^(11) N//m^(2), prop = 1.21xx10^(-5) ` per deg
`triangle theta=20^(@)C,mu=M/l=(0.1 kg)/1=0.1 kg//m `