Room modes occur when f =
(c/2)·√((nx/Lx)²+(ny/Ly)²).
Axial: one direction only (nx,0) or (0,ny). Tangential: two directions (nx,ny, both≠0).
Schroeder frequency f_s ≈ 2000√(RT60/V) marks the
transition to diffuse-field behaviour.
About Room Acoustic Modes
This simulation visualises the standing-wave pressure patterns that form inside a rectangular room when sound reflects between parallel surfaces. It models a two-dimensional cross-section, plotting the pressure field p = cos(nx·π·x/Lx) · cos(ny·π·y/Ly) · cos(ωt) as a colour map. Each resonance sits at the frequency f = (c/2)·√((nx/Lx)² + (ny/Ly)²), the eigenfrequencies of the room's acoustic geometry.
Sliders set the room length Lx, width Ly and the speed of sound c, while a grid of buttons selects individual modes ordered by frequency. Toggles animate the oscillating pressure, draw dashed nodal lines and show a draggable source marker. Modes are classified as axial, tangential or oblique. These resonances dominate low-frequency response in studios, listening rooms and small auditoria, where they cause uneven bass.
Frequently Asked Questions
What is a room mode?
A room mode is a standing wave that forms when a sound wavelength fits exactly between a room's reflecting surfaces, reinforcing certain frequencies and cancelling others. At these resonant frequencies the acoustic pressure builds to peaks at the walls and falls to zero along nodal lines, producing uneven loudness across the space.
What equation sets the modal frequencies?
For this two-dimensional model the frequency is f = (c/2)·√((nx/Lx)² + (ny/Ly)²), where nx and ny are integer mode numbers and Lx, Ly are the room dimensions. The speed of sound c (about 343 m/s at room temperature) scales every frequency, and larger rooms push modes lower.
What do the sliders and toggles control?
The Lx and Ly sliders resize the room from 2 to 15 m and 2 to 12 m, and the c slider varies the speed of sound between 320 and 360 m/s. Toggles animate the pressure oscillation, show the dashed nodal lines, and reveal a source marker you can drag with the mouse to reposition the sound source.
What is the difference between axial, tangential and oblique modes?
Axial modes involve one pair of surfaces, so only one mode number is non-zero, such as (1,0). Tangential modes involve two dimensions with both numbers non-zero. Oblique modes engage all three dimensions in a full room. Axial modes are usually the strongest and most audible because they concentrate energy along a single axis.
What are nodal lines and why do they matter?
Nodal lines are positions where the pressure stays near zero throughout the oscillation, shown here as dashed white lines. A listener or microphone placed on a node hears almost nothing of that mode, while positions at the antinodes hear it strongly. This is why bass response changes dramatically as you move around a small room.
What is the Schroeder frequency?
The Schroeder frequency marks the transition from distinct, well-separated room modes at low frequencies to a dense, overlapping diffuse field at high frequencies. The simulation estimates it as f_s ≈ 2000·√(RT60/V), assuming a reverberation time of 0.5 s and a ceiling height of 2.5 m. Below it, individual modes dominate the response.
Is this simulation physically accurate?
The modal frequencies and pressure patterns follow the standard rectangular-room wave equation, so the geometry is accurate. It is a simplified two-dimensional, lossless model: it ignores wall absorption, damping, finite mode bandwidth and modal coupling, and the Schroeder estimate uses assumed values. It is a clear teaching tool rather than a measurement-grade acoustic predictor.
Why does moving the source change what I hear in a real room?
A source placed at a pressure node of a mode cannot drive that mode efficiently, so it excites it weakly, whereas a source at an antinode, typically a corner, couples strongly. Dragging the source marker illustrates why loudspeaker and subwoofer placement has such a large effect on perceived bass evenness.
How does room size affect the modes?
Because frequency is inversely proportional to dimension, larger rooms have lower fundamental modes and a denser packing of modes at audible frequencies, which smooths the response. Small rooms have widely spaced low modes that create strong peaks and dips. Increasing Lx or Ly in the simulation shifts the listed mode frequencies downward accordingly.
Why do similar room dimensions cause problems?
When two or three room dimensions are equal or simple ratios of each other, several modes coincide at the same frequency, stacking up to create a pronounced resonance and a deep null elsewhere. Acousticians choose dimension ratios that spread the modes evenly, which you can explore by adjusting Lx and Ly and watching the mode list reorder.
How is this used in real-world acoustics?
Studio designers, home-cinema installers and concert-hall acousticians use modal analysis to choose room proportions, position loudspeakers and listeners, and place bass traps at high-pressure corners. Understanding where modes peak and null guides treatment so that low-frequency reproduction is even and accurate across the listening area.