The second harmonic of a guitar string has a frequency of 120 Hz. What is the length of the guitar string if the speed of the waves on the string is 110 m/s?

no

To find the length of the guitar string, we can use the relationship between frequency (f), speed (v), and wavelength (λ) of a wave:

v = f * λ

In this case, we are given the frequency of the second harmonic (f = 120 Hz) and the speed of the wave on the string (v = 110 m/s). We need to find the wavelength to determine the length of the string.

The second harmonic of a guitar string corresponds to half a wavelength. So, we can find the wavelength (λ) by dividing the speed of the wave by the frequency:

λ = v / f

Substituting the given values:
λ = 110 m/s / 120 Hz

Calculating the wavelength:
λ = 0.9167 m

Since the second harmonic corresponds to half a wavelength, the length of the guitar string would be twice the wavelength:

Length of the guitar string = 2 * λ
Length of the guitar string = 2 * 0.9167 m
Length of the guitar string ≈ 1.833 m

Therefore, the length of the guitar string is approximately 1.833 meters.

The third harmonic =>L=3λ/2 =3v/2f=

=3•125/2•170=1.103 m