# Exploring the Relationship Between String Tension & Audio Output Amplitude

• mikejm
In summary, the tension in a plucked or struck string will increase with amplitude, and this increase will decay quickly. It is important to model this decay to create accurate audio output.f

#### mikejm

I am working on a guitar/piano synthesizer for my own interest. When a string is plucked or struck, tension increases causing a slight pitch bend and change in the inharmonicity. This change then settles as the note quiets down. Thus it is important to model how the tension rises above baseline when a note is struck and evolves.

I have put a lot of thought into it and my presumption is that the tension increase from excitation must vary in some fairly direct manner with the amplitude of the total audio output signal of the string.

Let's say a string has a resting tension of 70 N with a resting audio signal output of amplitude 0. Let's say you then calibrate the simulation so an output amplitude of 1 corresponds to a tension increase to 72 N. Would there be a linear relationship between the tension and the amplitude changes, so that at an output of 0.5 there would be 71 N tension expected?

If not, how would the relationship likely work?

Thanks.

Now I'm actually thinking of it from a different perspective.

The tension that is increased at the point of plucking or striking a string is the potential energy that then creates the audio output, right?

So actually the tension should decay very rapidly back to the baseline as the sound "explodes" from plucking it.

I wonder if there's any way to model how quickly the tension would decay based on things like string diameter, tension, linear mass, etc.

Did you really mean inharmonicity? I would have guessed that wouldn't be significantly influenced by how hard you pluck a string.

http://www2.eng.cam.ac.uk/~jw12/JW%20PDFs/Guitar_II.pdf

That paper discusses the issues you ask about. I found it with an Internet search for "plucked string design".

And you would need significantly more than a single data point to test your theory.