In English: not only does the string vibrate as a standing wave along its whole length (the fundamental frequency), but also along half its length, a third of its length, etc. Giving us the frequency of the nth harmonic: Observe that the angular frequency in the above solution is Where Given some initial condition and for all x at t=0, the solution of the wave equation is In an ideal case, each individual guitar string obeys the wave equation: As a guitar player of nine years, I have always been aware of harmonics or “overtones” on guitar but did not always understand how they worked physically, which inspired this project. My goal with this project was simply to use Fourier analysis to explore the harmonics of guitar strings.
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