by

Ciro Santilli (@cirosantilli, 37)

Damped wave equation

Table of contents
- Plucked string model Damped wave equation

Plucked string model

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Staring from a triangle wave, this explains why we always get the same musical notes:

www.math.hmc.edu/~ajb/PCMI/lecture7.pdf "7.5.1. Musical instruments" is very good. Also mentions that in the piano it is more like an initial speed is applied, and it is not the same as plucking
music.stackexchange.com/questions/135635/confusion-about-overtones-and-a-slow-motion-video-of-a-plucked-string
music.stackexchange.com/questions/60833/what-determines-the-relative-volumes-of-the-harmonics-when-plucking-a-guitar-str

See also: solving partial differential equations with the Fourier series.

TODO: do higher overtones decay faster in time than the base ones?

www.physicsforums.com/threads/why-do-harmonics-decay-faster-than-the-fundamental.955731/ But presumaby yes, damping force is proportional to speed, and higher harmonics have higher speeds going up and down

Motion of Plucked String by Dan Russell

Slow motion: rubber string pulled and released by Pavel Radzivilovsky

Good symmetric example. But unfortunately the video is too short.

Featured at: www.reddit.com/r/Physics/comments/kyocxr/what_happens_when_a_plucked_string_is_released/

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