Question

A guitar string is 90 cm long and has a fundamental frequency of 124 Hz.Where should it be pressed to produce a fundamental frequency of 186 Hz??

Answer 1

Frequency f = 1/(2L) * sqrt(T/μ)
L = length of string.
T = tension in the string.
μ = linear density

f1/f2 = L2/L1

L2 = 90*124/186 = 60 cm.
Make string length = 60cm

Answer 2

gFrequency f = 1/(2L) * sqrt(T/μ)

Frequency f = 1/(2L) * sqrt(T/μ)L = length of string.

Frequency f = 1/(2L) * sqrt(T/μ)L = length of string.T = tension in the string.

Frequency f = 1/(2L) * sqrt(T/μ)L = length of string.T = tension in the string.μ = linear density

Frequency f = 1/(2L) * sqrt(T/μ)L = length of string.T = tension in the string.μ = linear densityf1/f2 = L2/L1

Frequency f = 1/(2L) * sqrt(T/μ)L = length of string.T = tension in the string.μ = linear densityf1/f2 = L2/L1L2 = 90*124/186 = 60 cm.

Frequency f = 1/(2L) * sqrt(T/μ)L = length of string.T = tension in the string.μ = linear densityf1/f2 = L2/L1L2 = 90*124/186 = 60 cm.Make string length = 60cm