Question

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

Answer 1

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