Question

A uniform metal wire has length 'L', mass 'M', and density 'ρ'. It is under tension 'T' and 'v' is the speed of transverse wave along the wire. The area of cross-section A of the wire is ______ 

Options

• T²ρV 

• `("v"^2rho)/T`

• `T/("v"^2rho)`

• Tv²ρ 

Answer 1

A uniform metal wire has length 'L', mass 'M', and density 'ρ'. It is under tension 'T' and 'v' is the speed of transverse wave along the wire. The area of cross-section A of the wire is `underline(T/("v"^2rho))`.

Explanation:

V = `sqrt(T/m)`  `[m = M/L = (ALrho)/L = Arho]`

∴ V = `sqrt(T/(Arho)`

∴ `V^2 = T/(Arho)`

A = `T/(V^2rho)`