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.

Software features:

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.
Gated frequency response calculation.

Important notice: This simulation does not substitute in-room measurements.

Version: 1.3
File Format: exe (32-bit, portable, no installation required)
Operating System: Windows 2000 or later
License: freeware
Download

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. (In a stereo system placing diffusers and porous sound absorbers on the wall behind the speakers is the least efficient way to improve room acoustics.)

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.

10cm vs. 0cm driver on-axis room response

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 ms to 50 ms.

If a notch is "filled" within 50 ms then it will not be audible.

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. On the other hand, absorption coefficient has little effect on early reflections when the absorption coefficient is lower than ~0.5. This behavior makes notches hard to manage.

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.

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 1kHz). 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.

More about baffle diffraction & baffle step (external links):
'The Edge' baffle diffraction simulator and baffle designer by Tolvan
Baffle Step Compensation by Rod Elliott (ESP)
Loudspeaker Diffraction Loss and Compensation by John L. Murphy (True Audio)

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 response of our hearing system is smoother in a diffuse field than in free-field. In diffuse field, the resonance peak around 2.5 kHz is slightly reduced and the notch between 5 kHz and 10 kHz is "filled". [1,2]

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 ~3 decibels due to reflections [3]. (the magnitude of the notch is about 2-3 dB, so irrelevant in domestic rooms.)

Conclusion: two identical frequency response captured by one microphone can cause different response in the ear. Two identical frequency response can sound slightly different.

[1] Fig. 8.2. on page 205 in ‘‘Psychoacoustics - Facts And Models‘‘, Zwicker, Fastl, 2007
[2] Measuring HRTFs of Brüel & Kjær Type 4128-C, G.R.A.S. KEMAR Type 45BM, and Head Acoustics HMS II.3 Head and Torso Simulators, Technical University of Denmark, 2011
[3] 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)