Problem $06.$ The highest and lowest notes on a standard tuned guitar string are two

octaves apart, meaning the high note has a frequency four times greater.

a Assuming the tension remains the same between the two strings, discuss and calculate

how a manufacturer might achieve this difference in pitch.

b Calculate the tension required to tune a steel string of density $$ and length $L,$ with

diameter $d$ such that the fundamental vibrates at a frequency $f_{E4}.$

c Where should the fifth fret be placed such that the shortened string with the same

mass density and tension on the shortened string produces the perfect fourth with a

ratio of $4$:$3$ in the pitch of the original open string.