Question

A piano string of 1.15m and a mass of 20 g is under a tension of 6.30 into 10 power 3N. what is the fundamental frequency of string when it is struck? What are the frequencies of next two harmonic

Answer 1

The fundamental frequency of string

$$f_1=\frac{v}{2L}=\frac{1}{2L}\sqrt{\frac{TL}{m}}$$

$$f_1=\frac{1}{2\times 1.15}\sqrt{\frac{6.30\times 10^3\times 1.15}{0.020}}=262\:\rm Hz$$

The next wto harmonics

$$f_2=2f_1=2\times262\:\rm Hz=523\:\rm Hz$$

$$f_3=3f_1=3\times262\:\rm Hz=785\:\rm Hz$$