Calculate the stress in a tight wire of a material whose Young's modulus is `19.6xx10^(11)("dyne")/(cm^2)` so that the speed of the longitudinal waves is 10 times the speed of transverse waves.

Explanation

The speed of transverse waves in string is
`c_1=sqrt((T)/(m))=sqrt((T)/(Ad))`
Where A is cross-sectional area and d is the density.
The speed of longitudinal waves in string is `c_2=sqrt((Y)/(d))`. We have,
`c_2=10c_1`
`impliessqrt((Y)/(d))=10sqrt((T)/(Ad))`
`implies`stress`=(T)/(A)=(Y)/(100)=19.6xx10^9("dyne")/(cm^2)`