The Physics of Sound Waves in Musical Instruments

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The sound produced by a musical instrument is primarily a combination of its fundamental frequency and its harmonics, rather than a single sound wave. The fundamental frequency, or ground frequency, has the largest amplitude and determines the perceived pitch, while harmonics contribute to the overall sound quality without altering the pitch. For example, the E string of a guitar produces an E tone at 82.41 Hz as its ground frequency, accompanied by smaller amplitude harmonics. The presence of these harmonics can make the sound appear "noisy" or "unclean," and different instruments exhibit varying levels of harmonic content. The discussion also raises questions about the relationship between harmonics and wave coherence, suggesting a connection between these concepts in physics.
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Is the sound of one note generated by a musical instrument an example of a single sound wave or a group of in-phase (coherent) sound waves?
 
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In practice, just about all sounds are actually wave packets (a group) with harmonics etc.
But the ideal of a single note is a single wave.
 
In short, the sound you hear from a musical instrument is composed of it's ground frequency (f_n), this being the frequency with the largest amplitude, which defines the pitch that you hear, and all of it's harmonics (n*f_n) where n is a whole positive number.

For example, if you pick the E string of a guitar, you will hear an E tone in the second octave (82.41 Hz) Because this is the ground frequency and thus the frequency with the largest amplitude. The harmonics are also present, but they are all of a smaller amplitude and do not alter the pitch of the tone since their amplitudes are smaller (decreasing as n increases i think). The harmonics do however make the note seem more "unclean" or "noisy" than if it was only the E tone present, without the harmonics. I do think however that some instruments play their notes with more or less "harmonics pollution".
 
Do harmonics relate to wave coherence? In other words, are the sound waves in this "harmonic wave packet" said to be coherent in physics?
 
Harmonics, resonance, coherence -- are these related?
 

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