Room Boundary Simulator
Version: 1.3 (2023-05-02)
Software platform: Windows
Room Boundary Simulator is a simplified speaker placement simulator. Reflections from the floor, ceiling and from the wall behind the speaker can be analyzed.
- Following room reflections are simulated:
- reflection from the rear wall (wall behind the speaker);
- reflections from upper and lower corners of the rear wall;
- reflections between floor and ceiling up to the 4th reflection.
- The driver is modelled by a set of point sources (no cone 'break-up').
- Baffle step and rear response are predicted from the baffle width.
- Smoothing: 1/8 octave.
Important notice: This simulation does not substitute in-room measurements.
File Format: exe (32-bit, portable, no installation required)
Operating System: Windows 2000 or later
New in v1.3:
- Reflection between floor and ceiling is calculated up to the 4th reflection.
- Gated frequency response.
- Smoothing is enabled by default.
Examples, "case studies"
Wall behind the speaker has no effect on high frequencies
Baffle width is 20 cm, baffle step compensation is enabled, front of the cabinet is one meter from the rear wall. With a 20 cm wide baffle, the wall behind the speaker has no effect on the frequency response above 500 Hz. (Placing diffusers and porous sound absorbers on the wall behind the speakers makes no sense.)
Speaker driver diameter, directivity and on-axis room response
How does the directivity of speaker drivers affect the on-axis room response? 10cm speaker driver vs. point source analysis.
Only floor-ceiling reflections are modeled (no rear wall) and the focus of our interest is the region above 1 kHz. The room response is a combination of direct sound and sound radiated off-axis and reflected from the walls. Above 2 kHz the off-axis radiation from the 10cm driver gradually decreases and therefore the level of reflections is reduced. Around 10 kHz the radiation angle is so narrow that only the direct sound is captured by the microphone.
What is really interesting is that the falling response above 2 kHz in the 10cm driver's response is largely caused by the first reflection from the floor and the first reflection from the ceiling. The contribution of the late reflections to the slope is minimal.
How does frequency response change over time?
When the first reflected wave (usually from the floor) arrives at the microphone or the ear drum, it creates a strong comb filtering pattern. Then, the second reflection creates a similar pattern, but due to the longer path way the pattern moves down in frequency. Depending on the path difference the second reflected wave partially fills the notch created by the first reflection. This process is repeated over and over with longer path ways and decreasing amplitude. As a result, large notches created by early reflections are partially filled in the steady state response.
In the simulation we can see this process by selecting "Gated frequency response" and increasing the gate value from 1 msec to 50 msec.
Some notes on room acoustics
Why are reflections from near boundaries are worse?
In free field the sound pressure level generated by a point source is inversely proportional to distance (spherical radiation). This relation is also valid for reflected sound waves, if we replace distance with the path length travelled by the reflected wave. (However, not valid for the overall sound pressure level in a room, which is the sum of the direct and reflected sound.)
The magnitude of the notch in the gated response depends on the level difference between the direct and reflected wave. Higher the difference, lower the contribution of the reflected wave to the response and lower the magnitude of the resulting notch. The level difference is the ratio of the distance travelled by the direct wave and the reflected wave. When the loudspeaker is close to a boundary, the ratio will be close to one and the level difference will be close to 0 dB.
Sound absorption coefficient
The room's mean sound absorption coefficient has a large effect on late reflections and reverberation time (RT60). Doubling the mean absorption coefficient halves the reverberation time. Sound absorption coefficient also has a moderate effect on the magnitude of standing waves.
However, when the absorption coefficient is lower than ~0.5, changing the absorption in the room has little effect on the frequency response and sound pressure level. Though this behavior makes notches hard to manage, on the other hand, small changes in the absorption will not reflected in the frequency response.
Sometimes the effect of absorption is contrary to expectation and increasing an absorption coefficient makes the frequency response worse. Since the reduction of late reflections is greater than the reduction of early reflections, the notch created by a strong floor reflection may become larger.
Audibility of reflections
The human auditory system has an amazing ability to differentiate between lateral and frontal/rear reflections. This applies to both early and late reflections.
Reflections coming from the side (relative to the listener) don't change the tonality of the sound source. Side reflections may cause image shift and increase the sense of space, depending on their level. This also explains why DSP room correction doesn't work as expected, since correcting a lateral reflection definitely result in an unwanted spectral change.
To sum it up, only reflections from the floor, ceiling and back/front walls are relevant for spectral analysis.
Temporal integration (monaural)
The shortest temporal integration time of the human auditory system can be measured with pulses or pulse series. The temporal integration for pulses is quite short, it is about 5ms. Since we don't listen to pulses in an anechoic environment, 10 ms or 15ms time-window in gated measurements is more practical for characterizing the perceived spectrum of transients.
With arbitrary sounds (anything except pulses) the temporal integration depends on the envelope of the signal (envelope: duration of attack, decay and sustain). The envelope of the incoming sound also determines whether the reverberation of the room is heard as reverberation or spectral coloration. For example, in a small 20 m2 - 30 m2 room, reflections can be heard as a reverb after impulsive sounds (clap, percussion), but non-side reflections cause spectral coloration in slowly varying or sustained sounds. (Side note: usually reverberation is not an issue in domestic spaces.)
Baffle step in rooms
In free-field baffle step is a 6 dB rise in the frequency response between 100 Hz and 1 kHz (or a 6 dB loss below 500Hz). In sound-reflecting spaces baffle step is more complicated, as the magnitude of the "step" changes as we move away from the loudspeaker. The rear wall also has an effect on the baffle step. Moving away from the speaker in a room, the baffle step drops from 6 dB to 3 dB, which also means that 6 dB compensation is just a bit more than necessary. If a loudspeaker is mounted in a wall or a speaker with width/depth ratio higher than 1.5 is mounted on the wall, then baffle step compensation is not required (however, such placement may boost standing waves).
Baffle step and rear radiation are closely related phenomena. Rise in the front response corresponds attenuation on the rear. Also, baffle step and cut-off frequency of the rear radiation are controlled by the dimensions of the baffle. Since cabinets have very little sound radiation above 500 Hz to the rear, diffusers and porous sound absorbers on the wall behind the speakers do neither good nor harm.
Diffuse field vs. free-field
The human ear is not equally sensitive to sounds coming from different directions and the direction dependence is a function of frequency. A diffuse sound field causes a slightly different response in the ear than pure frontal waves . The difference is small and mainly affects the frequency range above 5 kHz. Around 10 kHz the diffuse-averaged ear response (diffuse HRTF) is 5 decibels more than the frontal response.
In a stereo system room absorption affects the magnitude of the 'stereo dip' at 2 kHz as well. What makes the stereo dip really interesting is that the dip is not present in measurements made with one microphone, only in artificial head measurements. Without room reflections the magnitude of the stereo dip in a dummy head measurement is about 10 decibels, in a "live" room the stereo dip is lowered to 5 decibels due to reflections .
Conclusion: two identical frequency response captured by one microphone can cause different response in the ear. Two identical frequency response can sound slightly different.
 Fig. 8.2. on page 205 in ‘‘Psychoacoustics - Facts And Models‘‘, Zwicker, Fastl, 2007
 Chapter: 9.1.3 An Important One-Toothed Comb - A Fundamental Flaw in Stereo in ‘‘Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms‘‘, Floyd E. Toole (Amazon link)