1. Chapter 11 Room Acoustics I: Excitation of the Modes and the Transmission of Impulses

2. Starting Ideas  Rooms are 3D and they contain air  Air has elasticity ("stiffness") It can be compressed and expanded  Air has mass  Air must support modes of vibration

3. Dynamic Microphone

4. Condenser Microphone

5. Human Ear

6. Sound Waves to Pressure Waves  Sound is a longitudinal disturbance Compressions result in higher pressure Rarefactions result in lower pressure  Pressure changes and particle motions give the same result.

7. An Experimental Source  Methods of introducing a quantity of air into a room Pop a balloon filled with air Explode a firecracker  We will use a pump that alternately injects and exhausts air to/from the room at a certain frequency.

8. Loudspeaker

9. Simple Source  Aperture for the source (size of the speaker) is small compared to the wavelength. analogous to the use of narrow plectra in plucking strings Ex. Wavelength for A 440 Hz is… v = f = 345 m/s, so  = v/f = 0.784 m

10. Loudspeakers as Sources  Loudspeakers are wide enough to not qualify as simple sources at high frequency, when the wavelength is short. for 10,000 Hz is 0.035 m  Speaker cone acts like a mass on a spring, with its own resonance behavior.

11. Source Notes  Locate at antinode to stimulate a room mode  Locate at node to suppress room mode Large numbers of modes stimulated together Hard to isolate one mode  Best response when source frequency matches mode frequency – resonance T ½ is long and W ½ is small

12. Room Modes  Room modes are approximately sinusoidal regardless of the driving frequency. There is a transient at the natural frequency and a steady state frequency at the driving frequency.

13. Interchangeability  Source (simple) and detector (microphone) are interchangeable.

14. Room Modes  Number of modes  Room Volume (N  V)  Increasing the damping increases the bandwidth (D  W ½ ) and the number of modes excited (D  N)  Number of modes  Frequency 2 (N  f 2 )

15. Number of Modes

16. Room Transfer Response Function  Highly variable from place to place in the room.  Frequencies of good and poor response do not correlate for different locations

17. Examples The dashed line indicates the average response of the thousands of low amplitude modes that make up the background.

18. Adding Furniture or Moving Objects  When the microphone response is good for a particular frequency, moving around had little effect.  When the microphone response is weak, moving around the room has a major impact. Such null points are small and tend to be very dependent on frequency.

19. Hopeless?  How can we ever get good tone color if the mix of partials changes with source/detector position?  Obviously, we can distinguish individual instruments and/or voices in a room. We must have only a partial picture. Our ears have trained themselves to use the room acoustics, so one expects some regularity.

20. Experimental Results  Consider a room driven by sinusoidally varying flow  Frequency was 600 Hz Frequency is the same as when we found strong excitation of the modes

21. Strongly Excited Mode onoff Rapid growth to maximum (0.1 s) Characteristic decay with T ½ about 1/20 s 0.1 s

22. Weakly Excited Mode onoff At on we get a ragged transient decaying away in a few tenths of a second Another transient comes after the source is turned off of similar shape

23. Intermediate Excited Mode We see behaviors of both strongly and weakly excited modes.

24. Observations  Simple decay behavior is observed when the modes are strongly excited  When modes are weakly excited transients come in irregular bursts The various off-resonance modes have to cancel out the few resonant modes. The transient bursts are due to the collection of individual mode transients before they all cancel.

25. More Observations  The halving time is generally longer than expected The important room modes are all very close in frequency. They tend to pull out of step with one another, lengthening the halving time.  Moving the source and microphone to new locations changes everything The response is a function of the microphone’s location with respect to the nodes and antinodes of the source.

26. Impulsive Excitation  Imagine a pump set up to suck air and then push air into a room  The impulse might look like…

27. Changes in Response with Distance Source Impulse Nearby Response Farther Away And Farther Still

28. Room Response to Impulse  Response Delay Sound propagates outward at 345 m/s From the delays in the pickup, we could determine how far the microphone was from the source.  Each response starts with the downward pulse of the source What comes next depends on the location

29. Less Time Magnification And then even less… Looks like the decay of an impulsive sound

30. Average Room Results  Take many readings at different spots in the room Or by moving furniture  We would find an average decay curve with a very definite halving time Same halving time as for the strongly excited modes

31. Reverberation  Set up a source with frequency components of roughly equal amplitude and ranging over the desired frequencies  12%.  T rev is defined to be the time for the sound to decay to 0.001 its initial amplitude. T rev = 9.97 T ½ Experimentally, W ½ = 3.8/ T rev measured in Hz

32. Testing Noise  White noise has the same distribution of power for all frequencies, so there is the same amount of power between 0 and 500 Hz, 500 and 1,000 Hz or 20,000 and 20,500 Hz.  Pink noise has the same distribution of power for each octave, so the power between 0.5 Hz and 1 Hz is the same as between 5,000 Hz and 10,000 Hz.

33. White Noise

34. Pink Noise

35. Outdoor Reverberation  Outdoors acts like a room of infinite reverberation time (it never fills up)  At the same time it acts like a room with zero reverberation time (no ringing of the modes after the source is turned off)

36. Reflection Experiment  In our experiments the waveform was not maintained over distance  Imagine doing the experiment outdoors or in a room so big that sound doesn’t have a chance to reach the walls. Amplitude declines by a  1/d Shape remains the same Vortex box

37. Simple Reflection  Now put a wall near the microphone  There is a time delay for the reflected wave as well as a smaller amplitude a  1/d Absorption by wall

38. Waveform  If the wall is so close that the reflected wave arrives before the direct wave is passed, then we get…

39. Multiple Reflections and Scattering  The walls, floor, and ceiling will reflect and re-reflect the wave Superposition of all these gives the background, irregular signal. Wave shape is preserved in reflections  Furniture and people will scatter the sound without preserving the shape

40. Small Object Scattering  When the size of the object is much smaller than the wavelength of the sound, then the object acts as a new source of sound, scattering in all directions.  Huygens’ Principle Huygens’ Principle

41. Size of Objects  Average period of the transient above is about 0.0005 s Using the speed of sound, the source has to be about (345 m/s)(0.0005 s) =.17 m About the size of your head

42. Large Object Scattering  Sound no longer propagates uniformly in all directions as for small scatterer Can act as a sound block giving acoustical shadows

43. Summary  Reflection off of large, flat objects (walls) does not distort the signal. Follows the same Law of Reflection as light.  Small, compact objects act as new sources of sound, emanating a modified signal uniformly in all directions.  Large Objects (furniture) act intermediate between the walls and the small objects.

44. Summary (continued)  Acoustics pressure impulses move at the speed of sound.  Amplitudes of the signal is inversely proportional to the distance traveled.  Amplitudes also decrease due to absorption by the walls.

45. Home Testing  Use a small, hard-walled room  Find two or three singing pitches that make the room respond  Walk around to note that the response varies with location. Places of strong interaction between the voice and the room are…  Near a wall  In a corner between two walls  Junction of three boundaries

46. Improved Testing  Tape sinusoidal tones then play them back through one speaker while walking around the room recording the result with a mic. Hold the mic at arm's length to reduce the scattering effects off your body. Defeat any auto level control on the tape recorder.