EE599-020Audio Signals and Systems

Room Acoustics

Kevin D. DonohueElectrical and Computer Engineering

University of Kentucky

Related Web SitesSetting up listening rooms and designing studios is a topic of interest for many hobbyists and audio professionals. Related websites can be found at:

http://www.rainfall.com/cdroms/audio_instructions.htm

http://www.silcom.com/~aludwig/Room_acoustics.html

http://home.tir.com/~ms/roomacoustics/roomacoustics.html

http://www.etfacoustic.com/

A standard room noise criteria (NC) has been established to describe or specify limits on room noise by assigning a number to a particular room-noise-like spectrum shown in figure below. Quiet is consider anything below NC 30. Source of noise include traffic, wind, HVAC, motors, business machines, conversations ...

Room Noise

32 64 128 256 512 1024 2048 4096 819210

20

30

40

50

60

70

80

90

Hertz

dB

NC 70

NC 45

NC 30

NC 25

NC 15

Sound barriers can be set up to block noise from external sources. The transmission loss through a barrier is given by:

where TL is the transmission loss in dB and M is the surface density in pounds per square foot (can be obtained by the product of the thickness and cubic density). Frequency (f in Hertz) dependence can be approximately accounted for by:

Typical material densities (lb/ft3) are:

Room Noise Blocking

23514 10 )(log. MTL

16514 10 )(log. MfTL

Brick Concrete

(Light)

Glass Gypsum Plywood Plexiglass Steel Lead Wood Rubber

120 100 180 50 36 74 480 700 24-28 57

http://physics.nist.gov/cgi-bin/Star/compos.pl?matno=001

While stopped at a traffic light in your car with windows open, another motorist pulls behind you with a loud stereo playing music where the bass player is stuck on a note corresponding to a frequency of about 78 Hz. If you rolled up your windows, how thick would your glass have to be to drop the bass sound by 30 dB (neglect the sound through the steel and rubber exterior materials). What thickness would be required for same attenuation of a tone at 261 Hz?

Example

If we wanted to run our glass breaking experiment inside a plexiglass chamber, determine the thickness needed to reduce the external sound level to 80 dB or less for a maximum internal sound level of 110 dB. Assume the base of the box is open to the floor and attenuation through the floor is negligible (relative to 80 dB). The lowest frequency to be used in this box is 500 Hz.

Homework (1)

For internal noise generation the object is to attenuate/absorb the noise energy as efficiently as possible. Sound impinging on surfaces in the room will be absorbed, reflected, or diffused.

Reflection and Absorption

Heat

DirectSound

Absorption

DirectSoun

d

Reflection

SpecularReflected

Sound

DirectSoun

d

Diffusion

DiffuseScattered

Sound

Transmission

Reflected and reverberant sounds can become distractions and annoyances. The use of absorbers on reflective surfaces can cut down the reverberation effects in rooms.

The model for a signal received at a point in space from many reflections is given as:

where n is scaling that represents the attenuation of each reflected signal due to propagation through the air and absorption at each reflected interface and n is the time delay associated with the travel path from the source to the receiver. The signal in the frequency domain is given by:

Reflection Absorption Effects

N

nnn tstr

1

)()(

N

nnn fjfSfR

1

2 )exp()()(

Reverberant Sound Travel

LS

EF1

EF2

EF3

EF4

RF2

RF1

RF3

D

The near or direct field (D)The free or early field (EF1 and EF2)The reverberant or diffuse field (RF1 to RF3)

Decay of Reverberant Sound Field

Time

Sou

nd L

evel

Direct Sound

Reverberation

Initial Time Delay Gap

60 dB

Reverberation Time

The time it takes for the reverberant sound field to decayby 60dB has become a standard way to characterize room acoustics.

For a space with many randomly distributed reflectors (typically large rooms) reverberation time (RT60 ) is defined as the amount of time for the sound pressure in a room to decrease by 60 dB from its maximum. The time is statistically predicted from the room features with the Sabine equation:

where V is the volume of the room in cubic meters Si is the surface area of the ith surface in room (in square meters) ai is the absorption coefficient of ith surface m is the absorption coefficient of air.

Discuss: The relationship between absorption, volume, and RT.

Room Reverberation Time

VfmfaS

VfRT

N

i

ii )(4)(

161.)(

1

60

Room Response to White Noise Input

Data collected and spectrogram computed by H.L. FournierNote frequency dependence on of decay time.

ExampleGiven the simulated reverb signal compute the RT60. Find the autocorrelation function and try to estimate the delays associated with the major scatterers.

% Create reverb signal

[y,fs] = wavread('clap.wav'); % Read in Clap sound

% Apply simulated reverb signal

yout1 = mrevera(y,fs,[30 44 121]*1e-3,[.6 .8 .6]);

taxis = [0:length(yout1)-1]/fs;

% Compute envelope of signal

env = abs(hilbert(yout1));

figure(1)

plot(taxis,20*log10(env+eps)) % Plot Power over time

hold on

% Create Line at 60 dB below max point and look for intersection point

mp = max(20*log10(env+eps));

mp = mp(1);

dt = mp-60;

plot(taxis,dt*ones(size(taxis)),'r'); hold off; xlabel('Seconds')

ylabel('dB'); title('Envelope of Room Impulse Response')

% Compute autocorrelation function of envelop and look for peaks % to indicate delay of major echoes

maxlag = fix(fs*.5);

[ac, lags] = xcorr(env-mean(env), maxlag);

figure(2)

plot(lags/fs,ac)

xlabel('seconds')

ylabel('AC coefficient')

% Compute autocorrelation function of raw and look for peaks to

% indicate delay of major echoes

[ac, lags] = xcorr(yout1, maxlag);

figure(3)

plot(lags/fs,ac)

xlabel('seconds')

ylabel('AC coefficient')

Room ModesThe air in a (small) rectangular room has natural modes of vibration given by:

where c is the speed of sound in the room p, h, and r are integers 0,1,2, …., and L, W, and H are the length, width, and height of the room.

222

2

H

r

W

q

L

pcf

ExampleGenerate a frequency sweep signal from 20 Hz to 15000 Hz that sweeps at a rate of 1000 Hz per second, record the signal and identify modes of the room.

Homework(2)Use data collected from the previous example to build a filter that undoes (deconvolves) the mode effects of the room.