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

2. Physics 1251Unit 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. f mean = (f 1 + f 2 )/2 = (262 + 264)/2 = 263 Hz f beat = ⃒f 1 - f 2 ⃒ = ⃒262-264 ⃒ = 2 Hz.

3. Physics 1251Unit 2 Session 18 Room Acoustics Reflective Review: Wave motion is characterized by Wave motion is characterized by ReflectionReflection RefractionRefraction DiffractionDiffraction Doppler ShiftDoppler Shift BeatsBeats InterferenceInterference The Reflective RefDifferedDopily,BeatingInterference.

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

5. Physics 1251Unit 2 Session 18 Room Acoustics Refraction occurs when a wave “enters” a medium that has a different velocity? Refraction V 1 < V 2

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

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

8. Beats f 1 f 2 Physics 1251Unit 2 Session 18 Room Acoustics In phase Out of phase f mean f beat

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

10. 1′ Lecture: Factors that most determine room acoustics: Direct sound Direct sound Reverberant sound Reverberant sound Freedom from echo and interference Freedom from echo and interference Background noise level Background noise level

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

12. Physics 1251Unit 2 Session 18 Room Acoustics ConstructiveInterference

13. Greek Amphitheater Acoustics Direct sound Reflected sound

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

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

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

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

18. Physics 1251Unit 2 Session 18 Room Acoustics 80/20 Standards for “Good” Acoustics: Clarity Clarity Uniformity Uniformity Envelopment Envelopment Smoothness Smoothness Reverberation Reverberation Performer satisfaction Performer satisfaction Freedom from noise 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 1251Unit 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 1251Unit 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. Speaker Hearer Physics 1251Unit 2 Session 18 Room Acoustics Room Acoustics: Reverberation Direct Sound Reverberant Sound

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

23. Physics 1251Unit 2 Session 18 Room Acoustics The intensity of the reflected wave is The intensity of the reflected wave is I reflected = (1-α) I in. I0I0I0I0 (1-α) I 0 (1-α) 2 I 0 (1-α) 3 I 0 (1-α) 4 I 0 (1-α) 5 I 0 (1-α) 6 I 0 (1-α) 7 I 0 (1-α) 8 I 0 (1-α) 9 I 0 (1-α) 10 I 0 (1-α) 11 I 0 (1-α) 12 I 0 αα

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

25. Physics 1251Unit 2 Session 18 Room Acoustics The Absorptivity Material α (at 500 Hz) Acoustic tile0.6 Plaster wall0.1 Concrete0.02 Person0.8 (x1 m 2 )

26. Physics 1251Unit 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?” 80/20 The reverberation time is the time for the intensity to decay by a factor of 10 –6 (- 60dB) of its initial value. WallaceSabine

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

28. Physics 1251Unit 2 Session 18 Room Acoustics 80/20 The Sabine Equation: I = I o ‧ 10 – 6 (t/T R ) T R = 0.16 V/S e V is the volume of the room. V is the volume of the room. S e is the “effective surface area” of the walls S 1, floor S 2 and ceiling S 3 (in sabin) etc. S e is the “effective surface area” of the walls S 1, floor S 2 and ceiling S 3 (in sabin) etc. α is the absorptivity of the surface (in table) α is the absorptivity of the surface (in table) S e = α 1 S 1 + α 2 S 2 + α 3 S 3 + α 4 S 4 +…

29. Physics 1251Unit 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: T R = 0.16 V/S e V is the volume of the room= 3x3x3 = 27.0 m 3. V is the volume of the room= 3x3x3 = 27.0 m 3. Walls S 1 = 4 (3x3 m 2 )= 36. m 2 ), Walls S 1 = 4 (3x3 m 2 )= 36. m 2 ), floor S 2 = 9.0 m 2 floor S 2 = 9.0 m 2 ceiling S 3 = 9.0 m 2 ceiling S 3 = 9.0 m 2 α = 0.02 S e = (0.02) (36.) + (0.02) (9.0) + (0.02) (9.0) = 1.02 sabine α = 0.02 S e = (0.02) (36.) + (0.02) (9.0) + (0.02) (9.0) = 1.02 sabine T R = 0.16 V/S e = 0.16 (27)/(1.02) = 4.2 sec

30. Physics 1251Unit 2 Session 18 Room Acoustics Summary: Direct sound should come first Direct sound should come first Haas or precedence effectHaas or precedence effect Reverberant sound Reverberant sound T R = 0.16 V/S eT R = 0.16 V/S e 0.8 sec for clear speech, 1-2 for music0.8 sec for clear speech, 1-2 for music Freedom from echo and interference Freedom from echo and interference Use diffuse and random reflectorsUse diffuse and random reflectors Background noise level Background noise level Assure good acoustic isolationAssure good acoustic isolation