Question

If a violin string vibrates at 195 hz as its fundamental frequency, what are the frequencies of the first four harmonics? first harmonic hz second harmonic hz third harmonic hz fourth harmonic hz

Answer 1

A violin is a both ends fixed, and so successive harmonics are simply multiples of the fundamental:

Therefore, f1 = 440Hz (fundamental frequency)

f2 = 2f1 = 2 x 440 = 880 Hz

f3 = 3f1 = 3 x 440 = 1320 Hz

f4 = 4f1 = 4 x 440 = 1760 Hz

Answer 2

The frequency of the nth-harmonic is n times the fundamental frequency f1:

`f_n = n f_1`
The first harmonic is the fundamental frequency:
`f_1 = 195 Hz`, then the following harmonics are

`f_2 = 2 f_1 = 2 \cdot 195 Hz = 390 Hz`

`f_3 = 3 f_1 = 3 \cdot 195 Hz = 585 Hz`

`f_4 = 4 f_1 = 4 \cdot 195 Hz = 780 Hz`