A load of 20kg is suspended by a steel wire in a sonometer experiment. Velocity of waves when the wire is rubbed with a resined cloth along the length is 20 times the velocity of waves in the same string, when it is plucked. Find area of cross-section of the wire, if Y for steel is `19.6xx10^(10)N//m^(2) and g =9.8m//s^(2)`.

Explanation

Here, `T=20kg=20xx9.8N.`
`Y=19.6xx10^(10)N//m^(2). g=9.8m//s^(2)`.
If a is area of cross-section of the wire, then mass per unit of wire, `m=axx1xxrho`
velocity of transverse waves,
`v_(t)=sqrt((T)/(m))=sqrt((T)/(arho))` …(i)
On rubbing with a resined cloth, longitudinal vibrations are produced in the string, where
`v_(L)=sqrt((Y)/(rho))`
As `v_(L)=20v_(t)`
`:. sqrt((Y)/(rho))=20sqrt((T)/(arho))`
`(Y)/(rho)=400xx(T)/(arho)`
`a=(400T)/(Y)=(400xx20xx9.8)/(19.6xx10^(10))`
`a=4xx10^(-7)m^(2)`