Fundamental Mathematics in Engineering II · Lecture 13 · demonstration
The overtones you hear are the modes you see
Each slider is one mode of the string — shape sin(kπx), pitch k×f0. Mix them, watch the string, then press play to hear that exact mix as timbre. Does changing the shape change the sound?
Mode k sounds at k×196 Hz (f0 = G3). Sound is synthesised on your device; your browser needs one click on play before it will make any.
How to read it
- Mode 1 only: a pure sine shape and a pure tone. Mode 2 only: the shape has a node in the middle — and the pitch is exactly an octave up.
- Pluck center: only odd modes appear, with weights 1, 1/9, 1/25, … — a hollow, flute-like tone. Pluck near end: many modes, a brighter, guitar-like tone. Same string; different shape; different sound.
- A string plucked once vibrates in all its modes at once. The mix of overtones you hear is the mix of mode shapes — that is Daniel Bernoulli's 1753 claim, made audible.
- What this mixer cannot make: a gong, a drum, or the sound "sh". Those need frequencies that are not multiples of one f0 — a continuum of them. That is the step from the Fourier series to the Fourier transform, later in the course.