THE NUMBERS, EXPLAINED
How to use this calculator.
Ideal uniform flexible string under tension (Mersenne's law); not a safety or instrument setup recommendation.
Start with your inputs
Enter vibrating length (m), target frequency (hz), linear density (kg/m). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Vibrating length (m) | 0.65 |
| Target frequency (Hz) | 440 |
| Linear density (kg/m) | 0.0005 |
A worked example
With the example inputs above, ideal tension (n) is 163.592. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Ideal tension (N) | 163.592 |
How this is calculated
Ideal tension (N)
tension_newtons (newtons): from f = (1/(2L)) * sqrt(T/mu), solve T = 4 * mu * L^2 * f^2 with L = length_m, f = frequency_hz, mu = linear_density_kg_m.
Symbols and units
- length_m
- Vibrating length (m)
- frequency_hz
- Target frequency (Hz)
- linear_density_kg_m
- Linear density (kg/m)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions and limits
Ideal uniform flexible string under tension (Mersenne's law); not a safety or instrument setup recommendation.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Ideal tension (N). The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Ideal uniform flexible string under tension (Mersenne's law); not a safety or instrument setup recommendation.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
UNSW Music Acoustics: strings, standing waves and harmonics ↗
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
Read the quality report →