Frequency Harmonics Calculator

Analyze fundamentals, overtones, and spacing with simple inputs. Compare open, closed, and string resonators easily. Export tables quickly for lessons, labs, revisions, and reports.

Calculator Input

Resonant System

Known Fundamental Frequency

Wave Speed

Resonator Length

Rows to Generate

Selected Harmonic

Fundamental Amplitude

Amplitude Decay Ratio

Phase Step per Series Position

Display Frequency Unit

Example Data Table

System	Wave Speed	Length	Fundamental	Shown Harmonics	Observation
String	343 m/s	1.2 m	142.917 Hz	1, 2, 3, 4	All harmonics appear in equal frequency spacing.
Open Pipe	343 m/s	0.8 m	214.375 Hz	1, 2, 3, 4	Open pipes behave like strings for harmonic order.
Closed Pipe	343 m/s	0.8 m	107.188 Hz	1, 3, 5, 7	Only odd harmonics are present in the series.
Generic Series	Not used	Not used	110 Hz	1, 2, 3, 4	Use this when fundamental frequency is already known.

Formula Used

Generic harmonic series: fₙ = n × f₁

String or open pipe fundamental: f₁ = v / 2L

Closed pipe fundamental: f₁ = v / 4L

Closed pipe harmonic rule: n = 1, 3, 5, 7, ...

Period: T = 1 / f

Wavelength: λ = v / f

Angular frequency: ω = 2πf

Amplitude estimate: A = A₁ × r^(position − 1)

Here, v is wave speed, L is length, f₁ is the fundamental, n is harmonic multiplier, and r is the decay ratio.

How to Use This Calculator

Select the resonant system that matches your physics problem.
Enter wave speed and resonator length to derive the fundamental automatically.
Or enter a known fundamental frequency directly.
Choose how many harmonic rows you want in the output table.
Set a selected harmonic to inspect one mode in detail.
Use amplitude decay and phase step for a richer series estimate.
Press the button to show the result block above the form.
Export the harmonic table using the CSV or PDF buttons.

Frequently Asked Questions

1. What is the fundamental frequency?

The fundamental is the lowest natural resonant frequency. Every higher harmonic is built from it.

2. Why do closed pipes use odd harmonics only?

A closed end forces a node while the open end forces an antinode. That boundary pattern removes even harmonics.

3. Can I use this for strings and air columns?

Yes. The calculator supports strings, open pipes, closed pipes, and a direct generic series model.

4. What happens if I already know the fundamental?

Enter the fundamental directly. The tool will skip derivation and build the harmonic series from your known value.

5. What does amplitude decay ratio mean?

It scales each next listed mode. A value below one makes higher harmonics smaller than the first.

6. Why does wavelength decrease for higher harmonics?

Wave speed stays fixed in one medium. When frequency rises, wavelength must shrink to keep v = fλ true.

7. What does phase step change?

It adds a constant phase difference between listed series positions. This is useful for quick waveform planning.

8. Can I export the results for reports?

Yes. Use the CSV button for spreadsheets and the PDF button for printable summaries and records.