Room acoustics
Sound source in a room
ƒ intensity increases quickly to equilibrium:
ƒ switched off then gradual decay
P
where A = ∑(αsiSi )
A
i
1.5
0
Intensity
Intensity
­ intensity ↓ by factor 106 1.0
­ sound level ↓ by 60 dB
0.5
-20
Sound level
-40
0.0
-60
-0.5
-80
-1.0
-100
0
2
Sound on
4
6
Time [s]
8
10
Sound level [dB]
ƒ Reverberation time RT
Iequil = 4
Room acoustics
Sabine’s empirical equation for RT
RT = 0.163 V/A
with
A = Σ (αsi Si)
ƒ depends on frequency
Room acoustics
Good acoustics
ƒ low background noise, loud wanted sound
ƒ well diffused sound field
ƒ no echoes or acoustic distorsions
ƒ appropriate RT
Room acoustics
Good acoustics
Geometrical acoustics
ƒ avoid large planar surfaces facing each other (fluttering echo)
ƒ avoid concave surfaces (focusing)
Bad
Good
Focusing (bad)
Distribution (good)
Image by MIT OCW.
Image by MIT OCW.
Room acoustics
Intelligibility and sound level
high sound level → low A → high RT → lower intelligibility
100%
Inteligibility
90%
80%
70%
60%
50%
40%
0
1
2
3
4
5
Reverberation Time [s]
Image by MIT OCW.
Optimal reverberation time [s]
Recommended RT
2.5
Music
Speech
2.0
1.5
1.0
0.5
0.0
200
500
1000 2000 5000 10000 20000
Room volume [m³]
Room acoustics
Intelligibility as a function of delay
Image by MIT OCW.
ƒ direct sound → path l
ƒ reflected sound → path l’
l'
Delay
l
ƒ ∆t =(l’ − l) / 340 [m/s]
ƒ Speech: ∆t ≤ 35 ms
i.e.
l’ − l ≤ 12 m (130 ms per syllable)
ƒ Music: ∆t ≤ 44 ms
i.e.
l’ − l ≤ 15 m
If critical
ƒ change room geometry
ƒ add absorbing panels
Room acoustics
Wave nature of sound
ƒ standing wave if L = n ½ λ
n=1
ƒ proper frequency fn = v/λn = n v/(2L)
→ no rational relationship between lengths
→ non-rectangular plan
n=2
B
S
W
l/2
n=3
L
L
Image by MIT OCW.
L = 1.2W
Image by MIT OCW.
Room Acoustics
Reading assignment from Textbook:
ƒ “Introduction to Architectural Science” by Szokolay: § 3.4
Additional readings relevant to lecture topics:
ƒ "How Buildings Work" by Allen: pp. 129-132 in Chap 14