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Room acoustics (3D)

About this app

An exhibition hall in 3D with two listening stations: materials for floor, ceiling and walls set the reverberation time after Sabine and Eyring and the reverberation radius. The floor map shows where station A is ahead of B or where direct sound outweighs reverberation. Early reflections run as rays via image sources, and an impulse response and a synthetic listening test make the difference audible.

Reverberation, absorption and critical distance

How long a room rings on depends on its volume and on how much sound its surfaces absorb. Sabine’s formula T = 0.161 · V / A relates the volume V to the equivalent absorption area A, the sum of area times absorption coefficient. For heavily damped rooms Eyring’s formula is more accurate. The critical distance r_H ≈ 0.057 · √(V/T) is the distance beyond which reverberation is louder than the direct sound. Further away you mainly hear the room, however loud the source is.

What the app shows

A box-shaped exhibition hall with two listening stations and a draggable listening position. For floor, ceiling and walls you choose materials from concrete and glass through parquet and carpet to curtain, acoustic panels and audience. The app computes reverberation time after Sabine and Eyring, the critical distance and the speech target from the German standard DIN 18041. A floor map shows where station A beats B, where direct sound dominates or how loud it is. Early reflections run as rays via image sources, with an impulse response of the first 300 ms.

What you can try

Load the examples: a hard foyer with glass walls reverberates for about 5.6 s, a damped hall with carpet, acoustic ceiling and curtain only about 0.46 s, while the critical distance grows from about 0.8 to 2.9 m. Change room size and materials and watch two stations in the same hall separate. Turn one station up: direct sound and reverberation rise equally, so their ratio stays the same. A synthesised listening test with claps or syllables lets you hear the difference.

Frequently asked questions

How do you calculate reverberation time with Sabine’s formula?
Sabine’s formula is T = 0.161 s/m · V / A, with room volume V in m³ and equivalent absorption area A = Σ αᵢ · Sᵢ in m², the sum of each surface area times its absorption coefficient. Reverberation time is how long the sound level takes to drop by 60 dB after the source stops. For example, a hall of 1000 m³ with A = 200 m² has T ≈ 0.8 s.
When should you use Eyring’s formula instead of Sabine’s?
Eyring’s formula T = 0.161 s/m · V / (−S · ln(1 − ᾱ)) uses the total surface area S and the mean absorption coefficient ᾱ. For small ᾱ both give almost the same result; in heavily damped rooms Sabine overestimates the reverberation time and Eyring is more accurate. Both assume a diffuse sound field, so rooms with very unevenly distributed absorption deviate from either.
What reverberation time is right for speech?
It depends on room volume and use. The German standard DIN 18041 gives a target for rooms used for speech and lectures (category A2) of T_target = 0.37 · lg(V/m³) − 0.14 s, which is just under 1 s for 1000 m³. Much longer times make syllables smear together, whereas early reflections arriving within about 50 ms of the direct sound support intelligibility.
What can I try in the room acoustics app?
In a 3D exhibition hall you set length, width and height and the materials for floor, ceiling and walls and see the reverberation time after Sabine and Eyring, the critical distance and the DIN 18041 target. Two listening stations and a listening position can be dragged around; the floor map shows where A beats B and where direct sound or reverberation dominates. Early reflections, an impulse response and a synthesised listening test make the room visible and audible.

Subject: Architecture & scenography

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