Question

The lowest string on a violin has a fundamental frequency of G-natural at 196 Hz. Which frequency represents the second harmonic of the string?

Answer 1

The frequency representing the second harmonic of the lowest string on a violin, with a fundamental frequency of G-natural at 196 Hz, is 392 Hz.

Step-by-step explanation:

The fundamental frequency of a vibrating string is the lowest frequency at which the string can oscillate. The second harmonic, also known as the first overtone, is the next higher frequency that the string can produce. To find the second harmonic frequency, we can use the formula:

`\[ f_n = nf_1 \]`

where
`\( f_n \)` is the frequency of the nth harmonic,
`\( n \)` is the harmonic number, and
`\( f_1 \)` is the fundamental frequency. In this case, we want to find the second harmonic
`(\( n = 2 \))`:

`\[ f_2 = 2 * 196 \, \text{Hz} = 392 \, \text{Hz} \]`

So, the frequency representing the second harmonic of the string is 392 Hz. This means that when the string vibrates at this frequency, it produces the second harmonic, which is one octave higher than the fundamental frequency.

In musical terms, the second harmonic corresponds to the note G an octave above the G-natural fundamental frequency. This doubling of frequency creates a higher-pitched sound that contributes to the rich and complex tones produced by a violin. Understanding the harmonic series and how frequencies relate to each other is crucial in both the physics of musical instruments and the art of music composition.