Question

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 andthe 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 onyour guitar to A (55.0 Hz). If your were to maintain the same tension in the string as with the E string, what diameter of string would you need to purchase to producethe desired note? (inches)
Unfortunately, none of the strings in your collection have such a large diameter. In fact, the largest diameter you possess is 0.06245 inches. If the tension on yourexisting string is denoted Tbefore, by what fraction will you need to detune (that is, lower the tension) of this string to achieve the desired A note?
Tafter/Tbefore=

Answer 1

suppose the sounds are being produced in the fundamental mode. then wavelength = 2L.
then by the formulae for frequency, f1 d1 = f2 d2. by substuting , we get
,A. d2= 0.074 inches.
B. consider the initial tension as T before.
then by substuting values we get
t after / t Before = 0.345