The third harmonic of a guitar string has a frequency of 170 Hz. What is the length of the guitar string if the speed of the waves on the string is 125 m/s?

1.103 m

2.206 m

0.368 m

2.040 m

Refer to the figure shown below.

At the 3rd harmonic, there will be 3/2 wavelengths over the length of the guitar string. That is,

L = (3/2) λ

where

L = length of guitar string

λ = wavelength

Note that v = fλ, where

v = wave velocity,

f = wave frequency,.

Therefore

L = (3/2) λ

= (3/2) * (v/f)

= (3/2) * (125 m/s) / (170 1/s)

= 1.1029 m

Answer: 1.103 m