quality of note depends on relative intensity of the modes of vibration??

Question

In my syllabus I am told to appreciate that the quality of the note from the stringed instrument depends on the relative intensity of the modes of vibration.

Could someone please explain this to me in English.

Answer 1

A "mode" is a vibration that changes in amplitude, but not spatial arangement. It's hard to describe all of this in plain English. A mode is a portion of sine-like waves. Imagine if you pluck a string and it forms just one type of vibration, that is the whole string just moves up, down, up, down, and this does not change. This would be the first mode of vibration. Now imagine you take the first half of the string, pull it down, take the second half and pull it up, and then let go, now the first half moves up, the second half moves down, the middle DOESN'T move, and then this just alternates. This is the "second mode" of vibration. Now here's where it gets more involved. There are an infinite number of these normal modes, that is, the one with one section that moves (first), the one with two sections that move (two), the one with 3, 4, 5, 6, . . . and higher frequencies. Each mode on it's own is of a SINGLE frequency, or pure tone. Nonetheless, any ARBITRARY waveform can be resolved into sums of the normal modes, with the proper amplitudes chosen for each frequency. A cheap example would be the first mode we talked about, where the only amplitude is in the first mode, and none in the rest. Most physical instruments produce waves of irregular shapes, which means they are sums of several of these modes, which results in over/under tones, due to the various frequencies of the modes which are needed to comprise the shape of the wave.