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.