Understanding Harmonics in Sound
A harmonic is a wave whose frequency is a positive integer multiple of the frequency of the fundamental wave. In sound, the fundamental frequency is the lowest frequency produced by a vibrating object, which is perceived as the pitch of the sound. Harmonics are naturally occurring overtones that are integer multiples of this fundamental frequency, creating the unique timbre or quality of a sound.
The Relationship to Overtone and Timbre
While often used interchangeably, 'harmonic' specifically refers to overtones that are integer multiples (2f, 3f, 4f, etc.) of the fundamental frequency (f). Other overtones, which are not exact integer multiples, are called 'inharmonic overtones.' The combination and relative intensity of these harmonics and overtones determine a sound's timbre, allowing us to distinguish between different instruments playing the same note.
A Practical Example: Musical Instruments
When a guitar string vibrates, it doesn't just vibrate at its fundamental frequency. It also vibrates in segments, creating harmonics. For instance, a string vibrating in two halves produces the second harmonic (octave), three halves produce the third harmonic (perfect fifth above the octave), and so on. These multiple vibrations occur simultaneously, contributing to the rich and characteristic sound of the guitar.
Importance in Acoustics and Signal Analysis
Understanding harmonics is fundamental in acoustics, music theory, and signal processing. In music, harmonics explain why different instruments sound distinct even when playing the same note, and how chords and intervals work. In engineering, analyzing harmonics helps in understanding signal purity, designing filters, and in fields like telecommunications and medical imaging where wave properties are crucial.