1. Physics of Music, Spring 2018
Room Acoustics
Physics of Music, Spring 2018

2. Visualizing Reflections

3. Sound Intensity Level SIL = 10 log10 (I1/Io) dB Io = 10-12 W/m2
unit = decibel
Io = W/m2
Factor of 10 increase  10 dB
Factor of 2 increase  3 dB
1 dB  I1/Io = 1.25
3 dB  I1/Io = 2
10 dB  I1/Io = 10
20 dB  I1/Io = 100

4. Reverb Time
RT60

5. Texture: Smooth Operator?
Ragged Decay Double-Slope
Strong echos
(usually bad)

6. Sabine’s Law RT60=55.2 𝑉 𝑣𝑠𝑜𝑢𝑛𝑑 𝑆𝑎 V = volume of room
Empirically derived formula for Reverb Time:
RT60=55.2 𝑉 𝑣𝑠𝑜𝑢𝑛𝑑 𝑆𝑎
V = volume of room
Sa = total absorption surface area =
a1 A1 + a2 A2 + a3 A3 + …
vsound ~ 343 m/s ~ 1100 ft/s
Wallace C. Sabine
“Father of Acoustics”

7. Chart for Coefficient of Absorption (a)

8. Example Problem (Lecture Hall)
40 ft
10 ft
20 ft
Tile floor (a = 1000 Hz)
Plasterboard Walls/Ceiling (a = 1000 Hz)

9. Famous Concert Halls: reverb time
Boston Symphony Hall: 1.8 s
Carnegie Hall, NYC: 1.7 s

10. Design Tradeoffs Fullness vs. clarity:
reflected sounds vs. direct sounds
Warmth vs. brilliance:
longer reverb time at lower frequencies vs. high frequencies
Intimacy:
Short delay time between direct sound and early reflections
Texture: avoid bad echos

11. Image Sources Cited D. Hall, Musical Acoustics