A uniform copper wire of length L , mass M and density `rho` is under a tension T . If the speed of the transverse wave along the wire is v, then area of cross section (A) of the wire is

Options

A. `(Tv^(2))/rho`
B. `T/(v^(2)rho)`
C. `(v^(2)rho)/T`
D. `(Trho)/v^(2)`

Answer

B

Explanation

For transverse waves on a wire ` v = sqrt(T/m) `
`m = M/L = (A L rho)/L = Arho `
` :. v = sqrt(T/m) = sqrt(T/(Arho))`
` :. v^(2) = T/(Arho) :. A = T/(v^(2)rho)`