Circular Membrane Fundamental Calculator
IdealclampedcircularmembraneaxisymmetricfundamentalfromfirstJ0zero,radiusnotdiameter,not flexuralplate. Actual matched calibration,units,edition,geometry/measurement and model applicability independently established;not hearing/structural safety,compliance or universal perceptual prediction.
Description
A tensioned circular membrane’s fundamental axisymmetric mode depends on radius, tension and areal mass.
A tensioned circular membrane’s fundamental axisymmetric mode depends on radius, tension and areal mass.1
This calculator uses the first zero of J0 for an ideally fixed boundary, rather than the bending stiffness of a circular plate.
When to use Circular Membrane Fundamental Calculator
Use this tool to apply the stated circular membrane fundamental calculator operation with an explicit input and unit basis.
How to use Circular Membrane Fundamental Calculator and how it works
- Establish the measurement basis and units described above.
- Enter actualMembraneRadius, actualUniformTensionPerLength, actualMembraneMassPerArea and run the tool.
- Read result.value using the output meanings below.
- If input is rejected, correct the stated type, range, ordering or alignment issue and rerun; review successful results under the declared convention.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualMembraneRadius | Membrane Radius. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; strictly positive; further conditions in the algorithm |
| actualUniformTensionPerLength | Uniform Tension Per Length. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; strictly positive; further conditions in the algorithm |
| actualMembraneMassPerArea | Membrane Mass Per Area. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; strictly positive; further conditions in the algorithm |
Require positive radius, uniform tension per length and mass per area in coherent units. Use the coefficient 2.404825557695773 divided by 2πradius times sqrt(tension/arealMass); SI units produce hertz.
f1 = 2.404825557695773/(2πradius) × sqrt(tensionPerLength/massPerArea) Apply the declared units, ordering and branch conditions.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the declared output fields. | object |
| result.value | Ideal frequency in Hz when all inputs use coherent SI units. | number |
{
"input": {
"actualMembraneRadius": 1,
"actualUniformTensionPerLength": 1,
"actualMembraneMassPerArea": 1
},
"output": {
"result": {
"value": 0.38273987478100624
}
}
}Limitations and assumptions
The output applies the declared operation to the values you supply. Establish the measurement basis, units, coefficients and any caller-selected rules before interpreting it. The tool does not independently collect or verify observations or decide whether a model or reference applies.
Supply explicit required fields with the documented types and dense aligned arrays. Unknown fields, wrong types and nonfinite numbers are rejected. Branch-specific constraints are explained above. A returned boolean, signed difference or tied result follows the stated convention; an input error instead means the required input contract was not satisfied. Very large inputs or outputs may be rejected by shared resource limits.
Alternative or Complementary methods
For a related operation, use Wall Coincidence Frequency Calculator. A thin plate’s critical coincidence frequency marks where bending-wave behavior interacts with sound radiation under an ideal model.
For a related operation, use Clamped Bar Fundamental Calculator. A cantilever bar has one fixed end and one free end, unlike a bar clamped at both ends.
References
-
Circular Membrane Fundamental Calculator — tool.io
Similar or alternative tools
- Wall Coincidence Frequency Calculator
A thin plate’s critical coincidence frequency marks where bending-wave behavior interacts with sound radiation under an ideal model.
- Clamped Bar Fundamental Calculator
A cantilever bar has one fixed end and one free end, unlike a bar clamped at both ends.