On a guitar, the lowest toned string is usually strung to the e note, which produces sound at 82.4 hz. the diameter of e guitar strings is typically 0.0500 inches and the scale length between the bridge and nut (the effective length of the string) is 25.5 inches.
various musical acts tune their e strings down to produce a \"heavier\" sound or to better fit the vocal range of the singer.
as a guitarist you want to detune the e on your guitar to a (55.0 hz).

if you were to maintain the same tension in the string as with the e string, what diameter of string would you need to purchase to produce the desired note?

assume all strings available to you are made of the same material.