Question

The extension in a wire obeying Hooke's law is x. The speed of sound in the stretched wire is v. If the extension in the wire is increased to 4x, then the speed of sound in a wire is

Options

• 2.5v

• 2v

• 1.5v

• v

Answer 1

2v

Explanation:

The speed of sound in a stretched wire is given by

`"v"=sqrt("T"/"m") or "v" prop sqrt"T"`

According to Hooke's law,
tension (T) ∝ extension (x)

`therefore "v"^'/"v"=sqrt("T"^')/sqrt"T"`

Given, T' = 4x and T = x

⇒ `"v"^'/"v"=sqrt(4"x")/sqrt"x"=2`

Or v' = 2v