The Physics of Sound Waves in Musical Instruments

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Discussion Overview

The discussion revolves around the nature of sound waves produced by musical instruments, specifically whether a single note is represented by a single sound wave or a collection of coherent sound waves. It explores concepts such as wave packets, harmonics, and coherence in the context of musical acoustics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that the sound of a musical note is ideally a single wave, while in practice, it is often a group of wave packets that include harmonics.
  • One participant explains that the sound from a musical instrument consists of a fundamental frequency (ground frequency) and its harmonics, with the fundamental frequency defining the perceived pitch.
  • There is a notion that harmonics contribute to the overall sound quality, making it seem "unclean" or "noisy," depending on their amplitudes relative to the fundamental frequency.
  • A question is raised about the relationship between harmonics and wave coherence, specifically whether the sound waves in a harmonic wave packet are considered coherent.
  • Another participant queries the connections between harmonics, resonance, and coherence, indicating a potential overlap in these concepts.

Areas of Agreement / Disagreement

Participants express differing views on whether a musical note is a single sound wave or a collection of waves, and there is no consensus on the relationship between harmonics and coherence. The discussion remains unresolved regarding these concepts.

Contextual Notes

The discussion does not clarify the definitions of coherence or resonance, nor does it resolve the implications of harmonics on sound quality and perception.

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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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