Spectral analysis of a chord plucked on an acoustic guitar and comparison to theoretical predictions based on the Fourier transform equations

Theoretically, the acoustics of string instruments are analyzed by calculating the harmonics of a vibrating string through solutions to the wave equation and through Fourier transforms. But the reality of observing the spectrums predicted directly from the recording of a plucked string is generally unsatisfactory and is often ignored. Students who are trying to grasp the physical concepts that are predicted are often confused by the spectra produced in a typical recording. This paper looks at the spectral analysis produced by a chord plucked on an acoustic guitar and its comparison to theoretical predictions based on the Fourier Transform Equations. What can be determined by observing the spectral data? Can we gain information about the chord played and perhaps how it was played by examining the spectral data? The spectral analysis of an A minor chord played on an acoustic guitar is used as an example of Fourier’s Theorem and verification of the Fourier Transform Equation applied to plucked strings. While the original objective of the study was to compare the spectrums produced in various room environments, upon analyzing the data, it was realized that the harmonic spectrum for each string is clearly shown for each note of the chord.