The speed of a transverse wave going on a wire having a length 50 cm and maas 5.0 g is `80ms^(-1)` The area of cross section of the wire is `1.0mm.^2` and its Young modulus is `16 xx 10^(11) N m^(-2).` Find the extension of the wire over its natural lenth.

Explanation

The linear mass density is
`mu = (5 xx 10^(-3))/(50 xx 10^(-2)) = 1.0 xx 10 ^(-2) kg//m`
The wave speed is
`v = sqrt((T)/(mu))`
Thus, the tension is `T = muv^(2)`
= `(1.0 xx 10^(-2)) xx 6400 = 64 N`
The Young' s modulus is given by
`Y = (T//A)/(AY)`
The extensio is, therefore, `Delta = (TL)/(AY)`
= `(64 xx 0.50)/(1.0 xx 10^(-6) xx 16 xx 10^(11))` = 0.02 mm