Waves
Waves are an integral part of the physics of string instruments.
Some important things to notice about how waves travel in
strings is that, if you stretch it more tightly, the wave speed
increases. The weight of the string also plays a part, the
thicker and heavier a string is, the slower the speed of the
wave. For now, I would like to talk about an interesting
phenomena that happens when you send a simple wave along the
string. For this discussion I would like to look at Fig. 1.
Fig. 1. Two traveling waves going in opposite directions (blue to the
right and green to the left) and their sum (red); time increases from top
to bottom, from Joe Wolfe, Strings, Standing Waves and Harmonics; 2016.
It is important to note for this as well that the wave is inverted, which means that " the blue plus green adds up to zero on the right hand boundary" (Wolfe, 2016). In basic terms, the green wave has the same frequency and amplitude, but in the opposite direction. Now, if you look at the diagram you'll see that at some points the string doesn't move at all. This normally occurs about half a wavelength apart and they are called nodes of vibration. Half way from the nodes are anti-nodes, which are points of maximum movement. Notice thought, that the peaks aren't moving along the string, these waves moving in opposite directions cause a standing wave. You can think of this as the fifth harmonic on a string whose length is the same as the width of the diagram.