Chapter 11 Room Acoustics I: Excitation of the Modes and the Transmission of Impulses.
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Transcript of Chapter 11 Room Acoustics I: Excitation of the Modes and the Transmission of Impulses.
Chapter 11
Room Acoustics I:Excitation of the Modesand the Transmission of
Impulses
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 stiffness coefficientfrequency =
moving mass
Dynamic Microphone
Condenser Microphone
Human Ear
Sound Waves toPressure Waves
Sound is a longitudinal disturbanceCompressions result in higher pressureRarefactions result in lower pressure
Pressure changes and particle motions give the same result.
An Experimental Source Methods of introducing a quantity
of air into a roomPop a balloon filled with airExplode a firecracker
We will use a pump that alternately injects and exhausts air to/from the room at a certain frequency.
Loudspeaker
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 stringsEx. Wavelength for A 440 Hz is…
v = f = 345 m/s, so= v/f = 0.784 m
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.
Source Notes Locate at antinode to stimulate a room
mode Locate at node to suppress room mode
Large numbers of modes stimulated togetherHard to isolate one mode
Best response when source frequency matches mode frequency – resonance
T½ is long and W½ is small
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.
Interchangeability
Source (simple) and detector (microphone) are interchangeable.
Room Modes Number of modes Room Volume
(N V)
Increasing the damping increases the bandwidth (D W½) and the number of modes excited (D N)
Number of modes Frequency2 (N f2)
Number of ModesRoom Mode Excitation
0
100
200
300
400
500
600
700
0 200 400 600 800 1000 1200
Excitation Frequency (Hz)
Nu
mb
er
of
Str
on
gly
Ex
cit
ed
M
od
es
Room TransferResponse Function
Highly variable from place to place in the room.
Frequencies of good and poor response do not correlate for different locations
Examples
The dashed line indicates the average response of the thousands of low amplitude modes that make up the background.
Adding Furniture orMoving 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.
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.
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
Strongly Excited Mode
on off
Rapid growth to maximum (0.1 s)
Characteristic decay with T½ about 1/20 s
0.1 s
Weakly Excited Mode
on off
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
Intermediate Excited Mode
We see behaviors of both strongly and weakly excited modes.
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.
More Observations The halving time is generally longer
than expectedThe 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.
Impulsive Excitation Imagine a pump set up to suck air
and then push air into a room The impulse might look like…
Changes in Response with Distance
Source Impulse
Nearby Response
Farther Away
And Farther Still
Room Response to Impulse
Response DelaySound propagates outward at 345 m/sFrom 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
Less Time Magnification
And then even less…
Looks like the decay of an impulsive sound
Average Room Results Take many readings at different
spots in the roomOr 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
Reverberation Set up a source with frequency
components of roughly equal amplitude and ranging over the desired frequencies 12%.
Trev is defined to be the time for the sound to decay to 0.001 its initial amplitude.
Trev = 9.97 T½
Experimentally, W½ = 3.8/ Trev measured in Hz
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.
White Noise
Pink Noise
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)
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/dShape remains the sameVortex box
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
Waveform If the wall is so close that the reflected
wave arrives before the direct wave is passed, then we get…
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
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
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 mAbout the size of your head
Large Object Scattering Sound no longer propagates
uniformly in all directions as for small scatterer
Can act as a sound block giving acoustical shadows
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.
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.
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
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.