Question

A guitar string has a mass of 3.5 g, a length of 60 cm and a tension of 380 N. These values produce a wave speed of 260 m/s.

Determine:

a) it’s fundamental frequency 

b) the frequency of the second harmonic 

c) the wavelength of the second harmonic. 

Answer 1

(a) We can find the fundamental frequency of the string as follows:

$$f_1=\dfrac{nv}{2L}=\dfrac{260\ \dfrac{m}{s}}{2\cdot0.6\ m}=217\ Hz.$$

(b) We can find the frequency of the second harmonic as follows:

$$f_2=2f_1=2\cdot217\ Hz=434\ Hz.$$

(c) We can find the wavelength of the second harmonic from the wave speed equation:

$$v=f_2\lambda_2,$$ $$\lambda_2=\dfrac{v}{f_2}=\dfrac{260\ \dfrac{m}{s}}{434\ Hz}=0.6\ m.$$