fundamental frequency of string

Question

A stretched string made of steel is vibrating at its fundamental frequency of 1500 Hz. What is the fundamental frequency of the second string made from the same steel, but which has a diameter twice that of the original and which is stretched by twice the force of the original?

Answer 1

f = 1/2L ( T/m) ^1/2

f is fundamental frequency

T = Tension on string

m = mass per unit length of string

m = density* Volume of string /L

= density*pi * radius^2/L

mass per unit length in second case

m’ = density * pi *4*radius^2/L

f’ = 2f