| Example | Lx (m) | Ly (m) | Lz (m) | Temp (°C) | Mode (nx,ny,nz) | Type | Frequency (Hz) |
|---|---|---|---|---|---|---|---|
| A | 5.0 | 4.0 | 2.8 | 20 | (1,0,0) | Axial | 34.30 |
| A | 5.0 | 4.0 | 2.8 | 20 | (0,1,0) | Axial | 42.88 |
| A | 5.0 | 4.0 | 2.8 | 20 | (1,1,0) | Tangential | 54.91 |
| A | 5.0 | 4.0 | 2.8 | 20 | (0,0,1) | Axial | 61.25 |
| A | 5.0 | 4.0 | 2.8 | 20 | (2,0,0) | Axial | 68.60 |
| A | 5.0 | 4.0 | 2.8 | 20 | (1,0,1) | Tangential | 70.20 |
For a rectangular box with dimensions Lx, Ly, and Lz, the modal frequency for indices (nx, ny, nz) is:
- f is frequency in hertz (Hz).
- c is the speed of sound (m/s).
- nx, ny, nz are non‑negative integers, not all zero.
- Axial: one non‑zero index. Tangential: two. Oblique: three.
- Select units, then enter length, width, and height.
- Enter temperature to estimate the sound speed.
- Optionally enable the sound‑speed override and set c.
- Choose a maximum mode index and optional frequency limit.
- Press Calculate to view modes above the form.
- Use the download buttons to export CSV or PDF.
1) What “box frequency” means
A rectangular enclosure supports standing waves when sound reflects between parallel surfaces. These resonances are called room or box modes. Each mode is indexed by three integers (nx, ny, nz) that describe how many half‑wavelengths fit along length, width, and height. The calculator lists those modes in ascending hertz.
2) The core equation behind the table
Modal frequency depends on size and sound speed. When a dimension is smaller, its modes rise in frequency because wavelength must fit in a shorter distance. The formula combines all three dimensions using squared ratios, so the influence is proportional to (n/L)². That is why higher indices climb quickly.
3) Axial, tangential, and oblique modes
Axial modes involve one dimension only, so they are often the strongest. Tangential modes involve two dimensions and typically carry less energy. Oblique modes involve all three and are usually the weakest, but they can still cluster in the midrange when many indices are included.
4) Typical frequency ranges to watch
In small rooms and speaker boxes, the most noticeable resonances often occur below about 200 Hz. For example, a 5 m length produces a first axial mode near 34 Hz at 20°C. If you shorten that length to 2.5 m, the first axial mode doubles to roughly 68 Hz, which can be easier to hear.
5) Temperature and the speed of sound
Sound travels faster in warmer air. A practical approximation is c ≈ 331.3 + 0.606·T(°C). At 0°C, c is about 331 m/s, while at 20°C it is about 343 m/s. That difference shifts frequencies by roughly 3.6%, enough to matter in precise acoustic design and measurement.
6) Choosing a good maximum mode index
A larger “max mode index” finds more modes and better shows clustering, but it also increases the table size. For quick checks of low‑frequency behavior, values from 4 to 8 are common. For detailed analysis up to a few hundred hertz, values from 10 to 15 can be useful.
7) Using a frequency limit for practical output
A maximum frequency filter keeps the output focused. If you only care about bass behavior, set the limit to 150–250 Hz. For studio rooms, many practitioners review modes up to 300–500 Hz because higher modes become denser and are often handled with broadband absorption rather than targeted tuning.
8) Reading the wavelength column
Wavelength is λ = c/f. It helps you relate a resonance to physical size. If a mode wavelength is around 5 m, then features or placement changes on the order of 0.5–1 m can affect perceived response. Exporting CSV or PDF lets you compare designs and document iterations.
1) What is the difference between axial and tangential modes?
Axial modes use one dimension (one non‑zero index) and are often strongest. Tangential modes use two dimensions and typically have lower amplitude because energy spreads across more surfaces.
2) Why do I see many modes very close together?
As the mode indices increase, more combinations of (nx,ny,nz) exist, so frequencies crowd together. This clustering is normal, especially above a few hundred hertz in typical rooms.
3) Should I use temperature or a custom sound speed?
Use temperature for fast estimates in air. Use custom sound speed when you have measured c, or when modeling a different gas, humidity condition, or a controlled test setup.
4) Does this calculator include damping or absorption?
No. It predicts ideal modal frequencies only. Real spaces shift slightly and have finite bandwidth depending on wall losses, openings, absorption, and furnishings.
5) What units should I use for best accuracy?
Either is fine. Imperial inputs are converted to meters internally. Accuracy depends more on correct dimensions and sound speed than on the input unit system.
6) How many rows should I show?
For quick checks, 150–300 rows are usually enough. If you increase the mode index or remove the frequency limit, raise the row count to avoid truncation.
7) Can I use this for speaker cabinets?
Yes. Treat the internal cavity as a rectangular box approximation. Results help identify likely standing‑wave frequencies, but cabinet bracing, stuffing, and irregular shapes can shift and reduce peaks.