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)`.

Options

A. 11
B. 20
C. 15
D. 10

Answer

A

Explanation

`Delta l=alpha l Delta theta rArr Y=(.^(T)//_(A))/(.^(Deltal)//_(l))rArr T=YA(Deltal)/(l)rArr T=alpha YA Delta theta =48.4N ,v=sqrt((T)/(mu))=sqrt((48.4)/(((0.1)/(1))))=22m//s`
`:.` for fundamental note `l=(lamda)/(2) rArr lamda =2m rArr f=(v)/(lamda)=(22)/(2)=11Hz`.