Question

Two wires are made of the same material but the second wire has twice the diameter and twice the length of the first wire. When the two wires are stretched, and the tension in the second wire is also twice the tension in the first wire, the fundamental frequency of the first wire is 730 Hz. What is the fundamental frequency of the second wire? Answer in units of Hz.

Answer 1

Step-by-step explanation:

For frequency in a wire , the expression is

n =
`(1)/(2l) \sqrt{(T)/(m) }` , n is frequency , T is tension , m is mass of wire per unit length

`n = (1)/(2l) \sqrt{(T)/(\pi r^2) }` r is radius of the wire

For first the expression can be written as

730 =
`(1)/(2l) \sqrt{(T)/(\pi r^2) }`

For second wire

n =
`(1)/(2 *2 l ) \sqrt{(2T)/(4\pi r^2) }` length = 2l , tension = 2T , radius = 2r .

Dividing

n / 730 = 1 / 2 √2

= 1 / 2.828

n = 258.13 Hz