Question

A string of fixed length has a 2nd harmonic frequency of 680 Hz but when it is vibrating in the 3rd harmonic its wavelength is 0.52 m.

a) Calculate the 1st harmonic frequency.

b) Calculate the 3rd harmonic frequency.

c) Calculate the speed of the wave energy along this string.

Answer 1

a) We can find the 1st harmonic frequency from the formula:

$$f_2=nf_1,$$ $$f_1=\dfrac{f_2}{n}=\dfrac{680\ Hz}{2}=340\ Hz.$$

b) We can find the 3rd harmonic frequency from the formula:

$$f_3=nf_1=3\cdot340\ Hz=1020\ Hz.$$

c) We can find the speed of the wave energy along this string from the wave speed equation:

$$v=f_3\lambda_3=1020\ Hz\cdot0.52\ m=530.4\ \dfrac{m}{s}.$$