Question

A uniform metal wire has length L, mass M and density p. It is under tension T and v is the speed of transverse wave along the wire. The area of cross-section of the wire is ______.

Options

• `"T"/("v"^2rho)`

• `("v"^2rho)/"T"`

• T²ρv

• Tv²ρ

Answer 1

A uniform metal wire has length L, mass M and density p. It is under tension T and v is the speed of transverse wave along the wire. The area of cross-section of the wire is `underline("T"/("v"^2rho))`.

Explanation:

The speed of transverse wave along a wire is given by

v = `sqrt("T"/mu)`

where, µ = mass per unit length.

= volume of unit length × density

= area × density

∴ v = `sqrt("T"/("A"rho))`

`=> "A" = "T"/("v"^2 rho)`