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.

Room Boundary Simulator

Software features:

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

New in v1.3:

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.)

wall behind the speaker analysis

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 msec to 50 msec.

Some notes on room acoustics

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 sound-reflecting spaces baffle step (6 dB rise in the frequency response in free-field) is modified by boundary interference. If we want to measure the free-field baffle step in a small room (minimum 20 m2), then we have to set up the speaker cabinet far from the walls (somewhere in the middle of the room) and the microphone has to be placed closer than the half of the room height, but farther than the width of the cabinet

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 [1]. 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 [2].

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] 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)

Acoustical simulation (all software)