Enter Inputs
Example Data Table
| Input L (m) | Input T (N) | Input μ (kg/m) | f1 (Hz) | f2 (Hz) | f3 (Hz) | f4 (Hz) | f5 (Hz) |
|---|---|---|---|---|---|---|---|
| 0.65 | 80 | 0.004 | 108.79 | 217.57 | 326.36 | 435.14 | 543.93 |
These values assume fixed–fixed ends and uniform tension.
Formula Used
Wave speed
v = √(T / μ)
T is tension (N). μ is linear density (kg/m).
Resonant frequencies
Fixed–Fixed / Free–Free: fₙ = n·v / (2L)
Fixed–Free: fₙ = (2n−1)·v / (4L)
L is vibrating length (m). n = 1,2,3…
Related quantities
- λ (wavelength): λₙ = 2L/n for fixed–fixed, or λₙ = 4L/(2n−1) for fixed–free.
- ω (angular frequency): ωₙ = 2πfₙ.
- P (period): Pₙ = 1/fₙ.
How to Use This Calculator
- Enter the vibrating length L of the string section.
- Enter the string tension T and select the unit.
- Provide linear density μ directly, or compute it from mass and length.
- Select the boundary condition that matches your setup.
- Choose how many modes to compute and the decimals.
- Press Calculate to see results above the form.
- Use the CSV or PDF buttons to export the mode table.
For best accuracy, keep units consistent and measure the vibrating length carefully.