What I Heard from the P.D.E
John H. Riley · Mathematics Magazine · 2025
SummaryMotivated by an actual stringed instrument, we utilize the vibrating string partial differential equation to determine the effect of plucking a string at different places. Plucking corresponds to an initial condition for the equation which is continuous but not differentiable. This leads to a series solution. Analyzing the series shows how where a string is plucked affects its tone.