Calculator Inputs
Choose a calculation mode, enter vibration details, and submit to estimate the string tension from physical properties or direct line density.
Example Data Table
This sample table shows how different gauges, densities, lengths, and frequencies influence the estimated tension.
| Example | Length (m) | Frequency (Hz) | Gauge (mm) | Linear Density (g/m) | Tension (N) |
|---|---|---|---|---|---|
| Nylon lab string | 0.65 | 110 | 0.8 | 0.5781 | 11.8206 |
| Steel music wire | 0.33 | 440 | 0.3 | 0.5549 | 46.7945 |
| Bronze wound string | 0.6 | 147 | 0.6 | 2.4881 | 77.4234 |
| Polymer practice string | 0.5 | 220 | 0.7 | 0.4618 | 5.588 |
Formula Used
The calculator uses the wave relation for a stretched vibrating string. Frequency rises when tension rises and falls when the string becomes heavier.
Wave speed: v = (2Lf) / n
Tension: T = μv²
Direct combined form: T = μ[(2Lf) / n]²
Area from gauge: A = πd² / 4
Linear density from material: μ = ρA
Stress: σ = T / A
- L = speaking length of the vibrating section.
- f = measured frequency in hertz.
- n = harmonic number.
- μ = linear mass density in kg/m.
- ρ = material density in kg/m³.
- d = string diameter.
How to Use This Calculator
- Enter the vibrating length and choose its unit.
- Enter the measured frequency and harmonic number.
- Select either direct linear density or gauge plus material density mode.
- Add optional tensile strength, safety factor, and measured force.
- Press Calculate Tension to show results above the form.
- Review the summary table, uncertainty band, and Plotly graph.
- Use the CSV and PDF buttons to save the output.
FAQs
1. What does string gauge mean here?
Gauge is treated as the string diameter. The calculator converts that diameter to area, then uses material density to estimate linear mass density and tension.
2. Why does harmonic number matter?
Higher harmonics vibrate at higher frequencies for the same tension. The harmonic term adjusts the wave speed relation so the tension estimate stays physically correct.
3. When should I use direct linear density mode?
Use direct mode when the manufacturer already provides mass per unit length. It avoids estimating density from diameter and is usually better for coated or composite strings.
4. What length should I enter?
Enter the active vibrating length only. Do not include extra wrapped length, bridge overhang, or slack portions that do not participate in the standing wave.
5. Can this calculator compare measured and theoretical tension?
Yes. Enter a measured force in newtons and the tool will report the percentage difference between the measured value and the calculated vibration-based value.
6. What does the uncertainty band show?
It gives a quick tension range around the final answer using your chosen percentage. It is useful when length, frequency, or density values are only approximate.
7. Why is tensile strength optional?
Tension calculation does not require tensile strength. That input is only used to estimate allowable load and utilization when you want a simple safety check.
8. Does the graph use current inputs?
Yes. The graph keeps the current length, harmonic, and density fixed, then sweeps frequency to show how the tension curve changes around your selected point.