Frequency-Dependent Decay in Sympathetically Resonant Strings
Ashley Pacheco
Co-Presenters: Diana Medina, Edisson Guevara
College: The Dorothy and George Hennings College of Science, Mathematics and Technology
Major: Computational Science & Engineering - STEM 5 Year B.S./M.S.
Faculty Research Mentor: Edward Farnum
Abstract:
Musical notes are composed of different frequencies. Sympathetic resonance in a stringed instrument describes vibrations from main strings which excite the sympathetic strings, leading to a drone sound. We use a partial differential equation to demonstrate the external forcing, which results in strong resonance without physically plucking the strings. We use this model to optimize the efficiency and improve the prototypes using mathematical, physical, and analytical models.Our physical model resembles a harp, driven by a speaker connected to a controllable audio signal. We record an audio file, identify the dominant frequencies, and then use those to create a driving signal. This is played through the speaker to excite the instrument. We adjust the wave equation based on the results from physical models. Preliminary tests show that the resonance is feasible and often decays at different rates.We hypothesize that the response amplitude depends on the duration of the driving force. All configurations may not be equally excitable, and upper harmonics may not resonate. We will also adapt the wave equation to properly model frequency-dependent decay. Once we better understand the response from a controlled driving signal, we consider the much more complicated acoustic input signals from a trumpet.Keywords: wave equation, frequencies, mathematical model, physical model, sympathetic resonance, decay rates