A steel wire `0.72` m long has a mass of `5.0 xx 10 ^(-3) kg.` If the wire is under a tension of 60 N, what is the speed of transvers waves on the wire ?

Explanation

Change in length of wire,
`Deltal=l_(1)alphaDeltaT=1.8xx2.0xx10^(-5)xx(T_(2)-T_(1))`
`=1.8xx2.0xx10^(-5)[(234-300)]`
`=1.8xx2.0xx10^(-5)xx(-66)`
`=-0.0024" m"=-2.4xx10^(-3)m`
Negative sign represent the decrease in length and cross-sectional are of wire,
`A=(pid^(2))/(4)=(pi)/(4)xx(2xx10^(-3))^(2)`
`:.A=(3.14xx4xx10^(-6))/(4)=3.14xx10^(-6)m^(2)`
and Young.s modulus, `Y=((F)/(A))/((Deltal)/(l_(1)))=(Fl_(1))/(A Delta l)`
`:.F=(YADeltal)/(l_(1))`
`=(0.91xx10^(11)xx3.14xx10^(-6)xx2.4xx10^(-3))/(1.8)`
`=3.8298xx10^(2)`
`~~3.81xx10^(2)N`