# 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.
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.

## 1. How does the tension of a string affect the audio output amplitude?

The tension of a string directly affects the audio output amplitude by changing the frequency of the sound waves produced. When a string is tightened, it vibrates at a higher frequency, resulting in a higher audio output amplitude. Conversely, when a string is loosened, it vibrates at a lower frequency, resulting in a lower audio output amplitude.

## 2. What is the relationship between string tension and audio output amplitude?

The relationship between string tension and audio output amplitude is directly proportional. This means that as the tension of a string increases, the audio output amplitude also increases, and vice versa. This relationship can be seen in various string instruments, such as guitars and violins, where tightening or loosening the strings can produce different levels of audio output amplitude.

## 3. How does the material of the string affect the relationship between tension and audio output amplitude?

The material of the string can also affect the relationship between tension and audio output amplitude. Different materials have different densities and stiffness, which can impact the tension required to produce a certain audio output amplitude. For example, a steel string may require more tension than a nylon string to produce the same audio output amplitude.

## 4. Can the length of the string also affect the relationship between tension and audio output amplitude?

Yes, the length of the string can also affect the relationship between tension and audio output amplitude. In general, longer strings require more tension to produce the same audio output amplitude as shorter strings. This is because longer strings have a lower natural frequency, so more tension is needed to increase the frequency to produce a higher audio output amplitude.

## 5. How can the relationship between tension and audio output amplitude be applied in practical settings?

The relationship between tension and audio output amplitude can be applied in various practical settings, such as in the design and construction of musical instruments. By understanding this relationship, instrument makers can adjust the tension of strings to achieve the desired audio output amplitude. This knowledge can also be applied in the field of acoustics, where engineers can use tension adjustments to fine-tune the audio output of different string-based instruments in live performances or recording studios.

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