# Do string instruments really create standing waves or not?

I have seen similar questions regarding this but containing answers that somewhat disagree with each other which makes it hard for me to understand this.

My question is mainly about when plucking a string instrument at the end side of it, not in the middle. From several slowmotion videos, including this one and this one, I can see that this creates a single propagating wave that reflects back and forth.

If there is no periodic plucking, there is no way that this single propagating wave would interfere with itself to produce standing waves and thus harmonics. And yet, I keep reading that plucking a string instrument (once) would produce (a mixture of) harmonics. How is this possible with a single propagating wave that can not interfere with itself? Are there other conditions, other than interfering propagating waves, that produce harmonics?

• Are you familiar with Fourier analysis? The plucking pulse contains a wide mixture of frequencies, some of those are in harmony with the fundamental of the string. – PM 2Ring Sep 17 '19 at 22:04
• @PM2Ring I have read a bit about it. Someone showed this picture in his answer: physics.stackexchange.com/a/111916/143509. Two questions came up because of this: 1. Does that mean that these Fourier standing waves are actually by definition something else that are not caused by interfering propagating waves? 2. Can those Fourier standing waves actually be seen during the propagation of a single propagating wave ? – Phy Sep 17 '19 at 22:13
• Mathematically the harmonics are a multitude of solutions that all satisfy the wave equation (with boundaries). The superposition principle then demands the 'complete' solution is a sum of all these particular solutions (fundamental + harmonics). You can see the math in action here: sciencemadness.org/talk/… – Gert Sep 17 '19 at 22:13
• @Gert Thanks a lot for the link. One question though; does that mean that these Fourier standing waves are actually by definition something else that are not caused by interfering propagating waves? – Phy Sep 17 '19 at 22:24
• interfering propagating waves They're not relevant. As said above and shown in the link, the fundamental and harmonics are simply the MANY (infinite, in fact) solutions of the wave equation. These are then summated to provide the complete solution. This is remarkably similar to (some) analytical solutions of the Schrodinger Equation, which also yields an infinite number of particular solutions, to be summated. I suppose you could claim this summation is your interference but personally I don't think it's useful to do so. – Gert Sep 17 '19 at 22:57