Physics 1251 The Science and Technology of Musical Sound

1. Physics 1251The Science and Technology of Musical Sound Unit 2 Session 18 MWF Room Acoustics

2. Physics 1251 Unit 2 Session 18 Room Acoustics Foolscap Quiz: Two tones of frequency 262 Hz and 264 Hz are sounded. What do you hear? Answer: A single tone of frequency 263 Hz beating with a beat frequency of 2 Hz. fmean = (f 1+ f2)/2 = (262 + 264)/2 = 263 Hz fbeat = ⃒f 1- f2⃒ = ⃒262-264 ⃒ = 2 Hz.

3. Physics 1251 Unit 2 Session 18 Room Acoustics Reflective Review: • Wave motion is characterized by • Reflection • Refraction • Diffraction • Doppler Shift • Beats • Interference The Reflective Ref Differed Dopily, Beating Interference.

4. Physics 1251 Unit 2 Session 18 Room Acoustics When the surface is smooth we have “specular” (mirror-like) reflection. Reflection Smooth Surface Roughness ≲ λ

5. Physics 1251 Unit 2 Session 18 Room Acoustics Refraction occurs when a wave “enters” a medium that has a different velocity? Refraction V1 < V2

6. Physics 1251 Unit 2 Session 18 Room Acoustics Diffraction What happens when a wave “is partially obstructed?

7. Physics 1251 Unit 2 Session 18 Room Acoustics Doppler Shift: Moving source Lower f Higher f fobserver = fsource [v + vobserver] / [v – vsource]

8. Physics 1251 Unit 2 Session 18 Room Acoustics Beats f1 f2 In phase Out of phase fmean fbeat

9. Physics 1251 Unit 2 Session 18 Room Acoustics Interference Constructive Destructive Softer Louder

10. Physics 1251 Unit 2 Session 18 Room Acoustics 1′ Lecture: Factors that most determine room acoustics: • Direct sound • Reverberant sound • Freedom from echo and interference • Background noise level

11. Physics 1251 Unit 2 Session 18 Room Acoustics Greek Amphitheater At Epidauros, Greece

12. Physics 1251 Unit 2 Session 18 Room Acoustics Constructive Interference

13. Physics 1251 Unit 2 Session 18 Room Acoustics Greek Amphitheater Acoustics Reflected sound Direct sound

14. Physics 1251 Unit 2 Session 18 Room Acoustics Musiksvereinssaale Vienna

15. Physics 1251 Unit 2 Session 18 Room Acoustics Royal Festival Hall http://www.coxt.freeeserve.co.uk/hall.jpg

16. Physics 1251 Unit 2 Session 18 Room Acoustics Morton Meyerson Symphony Center Dallas, Texas

17. Physics 1251 Unit 2 Session 18 Room Acoustics Winspear Center Edmonton, Canada

18. Physics 1251 Unit 2 Session 18 Room Acoustics 80/20Standards for “Good” Acoustics: • Clarity • Uniformity • Envelopment • Smoothness • Reverberation • Performer satisfaction • Freedom from noise …little overlap of sounds …everywhere the same …sound from all directions …no echoes …appropriate length of time …reflected to stage …no competition

19. Physics 1251 Unit 2 Session 18 Room Acoustics Cardinal Principle of Room Acoustics The temporal, spatial, intensity and phase relationships between the direct and reflected sound ultimately determine the quality of the acoustics in a room. A room is an instrument that can dull the most illustrious performance by the most accomplished musician, or it can increase the pleasure of listening.

20. Physics 1251 Unit 2 Session 18 Room Acoustics 80/20 Haas or Precedence Effect The earliest sound that arrives determines the sense of the origin of a sound, even if the later (<100 ms) reflections are louder. The direct sound should arrive first.

21. Direct Sound Reverberant Sound Physics 1251 Unit 2 Session 18 Room Acoustics Room Acoustics: Reverberation Speaker Hearer

22. Physics 1251 Unit 2 Session 18 Room Acoustics Energy Lost in Reflections: • The sound reflects many times, each time losing energy to the reflecting surface. • The quantity α is the absorptivity of the surface. • The intensity of the sound that is lost in a reflection is ΔIlost = α Iin.

23. (1-α)11I0 α (1-α)9I0 (1-α)7I0 (1-α)5I0 (1-α)3I0 (1-α) I0 I0 (1-α)2I0 (1-α)4I0 (1-α)6I0 (1-α)8I0 (1-α)10I0 (1-α)12I0 Physics 1251 Unit 2 Session 18 Room Acoustics • The intensity of the reflected wave is Ireflected= (1-α) Iin. α

24. Physics 1251 Unit 2 Session 18 Room Acoustics • The intensity of the reflected wave is Ireflected= (1-α) Iin. • Values for α, the absorptivity, for many types of surfaces have been measured and appear in extensive tables.

25. Physics 1251 Unit 2 Session 18 Room Acoustics The Absorptivity Material α (at 500 Hz) Acoustic tile 0.6 Plaster wall 0.1 Concrete 0.02 Person 0.8 (x1 m2)

26. Physics 1251 Unit 2 Session 18 Room Acoustics Wallace Sabine (Harvard professor 1868-1919) Asked: “How long will it take for the sound to die down to 1 millionth (-60 dB) of the initial value?” 80/20The reverberation time is the time for the intensity to decay by a factor of 10 –6 (- 60dB) of its initial value. Wallace Sabine

27. Physics 1251 Unit 2 Session 18 Room Acoustics Intensity of Sound in a Room: ~ Io I = Io‧ 10 –6 t / TR t = ⅙ TR ~ 1/10 Io Pressure Amplitude t = ⅓ TR ~ 1/100 Io Time (ms) http://hybrid.colorado.edu/~phys1240/sounds.html

28. Physics 1251 Unit 2 Session 18 Room Acoustics 80/20The Sabine Equation: I = Io‧ 10 – 6 (t/TR) TR = 0.16 V/Se • V is the volume of the room. • Se is the “effective surface area” of the walls S1 , floor S2 and ceiling S3 (in sabin) etc. • α is the absorptivity of the surface (in table) Se = α1 S1 + α2 S2 + α3 S3 + α4 S4 +…

29. Physics 1251 Unit 2 Session 18 Room Acoustics What is the reverberation time for 500 Hz sound in a concrete room that is 3 x 3 x3 meters? • The Sabine Equation: • TR = 0.16 V/Se • V is the volume of the room= 3x3x3 = 27.0 m3. • Walls S1 = 4 (3x3 m2 )= 36. m2 ), • floor S2 = 9.0 m2 • ceiling S3 = 9.0 m2 • α = 0.02Se = (0.02) (36.) + (0.02) (9.0) + (0.02) (9.0) = 1.02 sabine • TR = 0.16 V/Se = 0.16 (27)/(1.02) = 4.2 sec

30. Physics 1251 Unit 2 Session 18 Room Acoustics Summary: • Direct sound should come first • Haas or precedence effect • Reverberant sound • TR = 0.16 V/Se • 0.8 sec for clear speech, 1-2 for music • Freedom from echo and interference • Use diffuse and random reflectors • Background noise level • Assure good acoustic isolation