A light primer on string vibration

[fazool]

I wanted to share some info that, I hope, will give some basic insight into some interesting aspects of string vibration.

Everyone understands the basic idea of natural frequency and strings vibrating with a sinusoidal shape.

When a string is vibrating, it is actually undergoing three different types of vibration – all simultaneously.

The first type of vibration is the common one that everyone is familiar with.

This vibration produces lateral motion of the strings. When you excite a string (hitting/plucking/strumming) the string vibrates back and forth. This is where most of the vibration happens. We can all see this and intuitively understand it.

There are two more types of vibration, however.

The second type of vibration is axial. This is where the string stretches and relaxes along its length. If you were to stretch a string and were able to “pluck” it by pulling it and letting go it would vibrate axially. This can be visualized like stretching a bungee cord or cutting a rubber band into one strip, then stretching it in a straight line. This action is closely coupled to the lateral vibration.

As the string vibrates laterally it stretches and relaxes the string axially. In other words, as the common vibration happens, that movement you see in the string has to come from somewhere. The string actually gets longer and shorter as it is vibrating laterally. The amount of this is a (non-linear) factor of the amplitude. The harder you pluck the string, the bigger its amplitude and the more it vibrates back and forth, so the more it has to stretch and relax axially. That’s why you will see strings register as slightly more sharp when you pluck them harder.

Now an interesting aspect of this axial vibration is that the saddle will see this as a rocking motion, not an up/down motion. That’s the principle behind Taylor’s newest behind-the-saddle ES pickup.

The third type of string vibration is torsional. In other structures, like your car engine’s crankshaft, this is a huge factor, because there are big, long “arms” twisting the shaft. On a guitar string, the radius of such is extremely small, making the torsional component probably essentially negligible. It is however, also excited by a (vector) component of the lateral vibration. As the string is excited back-and-forth (lateral), it will stretch and relax (axial) and it will also twist and untwist slightly (torsional).

The saddle will not “feel” torsional vibration but the bridge pins will feel that as it holds the string while it tries to twist and untwist.

Again, the torsional component is axial component is small and the torsional component is tiny. But I thought it might be helpful to explain these phenomena in a visual sort of way.