Room Acoustic Axial Standing-Wave Modes (f = c·n / 2L) & Schroeder Frequency Calculator

Find fundamental room standing-wave bass peaks (Hz) and the Schroeder modal transition frequency.

Fundamental Length Axial Mode (1,0,0)
31.18 Hz
Fundamental Width Axial Mode (0,1,0) 40.83 Hz
Fundamental Height Axial Mode (0,0,1) 63.52 Hz
Schroeder Crossover Frequency 160.17 Hz
Inputs
⚡ Scenarios:
m
Room length L in meters.
m
Room width W in meters.
m
Room ceiling height H in meters.
s
Room reverberation time RT60 in seconds.
Results & Graph
Fundamental Length Axial Mode (1,0,0)
31.18 Hz
Fundamental Width Axial Mode (0,1,0)
40.83 Hz
Fundamental Height Axial Mode (0,0,1)
63.52 Hz
Schroeder Crossover Frequency
160.17 Hz

Fundamental Length Axial Mode (1,0,0)

Graph 1 • Room Acoustic Modes & Schroeder • Domain Architecture & Live Telemetry Maps Room Length Meters, Room Width Meters, Room Height Meters through Room Acoustic Modes & Schroeder Formula.
Source / Tx Target / Rx Room Acoustic Modes & Schroeder Propagation Path Fundamental Length Axial M 31.18 Hz Fundamental Width Axial Mo: 40.83 Hz Fundamental Height Axial M: 63.52 Hz
Graph 2 • Fundamental Length Axial Mode (1,0,0) Across Room Length Meters Sweep (40% → 160%) Evaluates f_axial = 343 / (2 × Dimension_m); f_Schroeder = 2000 × √(RT60_sec / R across 7 operating points (current input highlighted).
0 Hz 42.87 Hz 85.75 Hz 77.95 2.20m 51.97 3.30m 38.98 4.40m 31.18 5.50m 25.98 6.60m 22.27 7.70m 19.49 8.80m
Graph 3 • Joint Sensitivity: Room Length Meters × Room Width Meters Compares Fundamental Length Axial Mode (1,0,0) when Room Width Meters is shifted +25% (solid) vs. −25% (dashed).
0 Hz 24.50 Hz 49.01 Hz --- Room Width Meters @ 75% 44.55 -30% 36.68 -15% 31.18 +0% 27.11 +15% 23.99 +30%
Summary: Fundamental axial standing waves occur at 31.2 Hz (Length), 40.8 Hz (Width), and 63.5 Hz (Height), with a Schroeder modal crossover at 160 Hz.
Summary: Fundamental axial standing waves occur at 31.2 Hz (Length), 40.8 Hz (Width), and 63.5 Hz (Height), with a Schroeder modal crossover at 160 Hz.
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Formula & Mathematical Methodology: Room Acoustic Modes & Schroeder Formula

faxial = 343 / (2 × Dimensionm)
fSchroeder = 2000 × RT60sec / RoomVolumem³
f_axial = 343 / (2 × Dimension_m); f_Schroeder = 2000 × √(RT60_sec / RoomVolume_m³)
  • roomLengthMeters: Room Length Meters (m)
  • roomWidthMeters: Room Width Meters (m)
  • roomHeightMeters: Room Height Meters (m)
  • targetRt60Seconds: Target Rt60 Seconds (s)

Rounding: Engineering outputs round to 2–3 decimal places; discrete material bag/unit counts round up via ceiling.

Worked Example: Engineering Scenario: Room Acoustic Modes & Schroeder

Find fundamental room standing-wave bass peaks (Hz) and the Schroeder modal transition frequency.

  1. Enter your system dimensions, electrical/RF ratings, or environmental conditions.
  2. Evaluate the governing equation: f_axial = 343 / (2 × Dimension_m); f_Schroeder = 2000 × √(RT60_sec / RoomVolume_m³).
  3. Inspect the primary design output, supporting allowances, and 3 SVG schematics.
Result: Computes Room Acoustic Modes & Schroeder via f_axial = 343 / (2 × Dimension_m); f_Schroeder = 2000 × √(RT60_sec / RoomVolume_m³).

Frequently Asked Questions

How does the Room Acoustic Axial Standing-Wave Modes (f = c·n / 2L) & Schroeder Frequency Calculator calculate results?

It evaluates f_axial = 343 / (2 × Dimension_m); f_Schroeder = 2000 × √(RT60_sec / RoomVolume_m³) directly in your browser and updates three custom SVG visualizations in real time.

Can I use Goal Seek to solve backwards for a required dimension or rating?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input parameter.

Does this engineering calculator work offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Science & Engineering · Optics, Photonics & Acoustics

Room Acoustic Axial Standing-Wave Modes (f = c·n / 2L) & Schroeder Frequency Calculator: inputs, method, and how to read the result

Find fundamental room standing-wave bass peaks (Hz) and the Schroeder modal transition frequency.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Room Length Meters: Room length L in meters.
  • Room Width Meters: Room width W in meters.
  • Room Height Meters: Room ceiling height H in meters.
  • Target Rt60 Seconds: Room reverberation time RT60 in seconds.

What the calculation includes

With the default values shown, Fundamental Length Axial Mode (1,0,0) is 31.18 Hz. The calculation follows Room Acoustic Modes & Schroeder Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Room Length Meters from 5.5 m to 6.05 m changes Fundamental Length Axial Mode (1,0,0) from 31.18 Hz to 28.35 Hz. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard NREL, IEEE, ASHRAE, and IRC design equations.
  • Verify final structural, electrical, and mechanical specifications against local building codes.

Scope: Global Engineering & Building Code Standard Check the assumptions and limitations against your situation before relying on the estimate.

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