1. EE599-020 Audio Signals and Systems Room Acoustics Kevin D. Donohue Electrical and Computer Engineering University of Kentucky

2. Related Web Sites Setting 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/

3. 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

4. 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/ft 3 ) are: Room Noise Blocking BrickConcrete (Light) GlassGypsumPlywoodPlexiglassSteelLeadWoodRubber 12010018050367448070024-2857 http://physics.nist.gov/cgi-bin/Star/compos.pl?matno=001

5. 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

6. 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)

7. 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 Direct Sound Absorption Direct Sound Reflection Specular Reflected Sound Direct Sound Diffusion Diffuse Scattered Sound Transmission

8. 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

9. Reverberant Sound Travel The near or direct field (D) The free or early field (EF1 and EF2) The reverberant or diffuse field (RF1 to RF3)

10. Decay of Reverberant Sound Field The time it takes for the reverberant sound field to decay by 60dB has become a standard way to characterize room acoustics.

11. For a space with many randomly distributed reflectors (typically large rooms) reverberation time (RT 60 ) 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  S i is the surface area of the i th surface in room (in square meters)  a i is the absorption coefficient of i th surface  m is the absorption coefficient of air. Discuss: The relationship between absorption, volume, and RT. Room Reverberation Time

12. Room Response to White Noise Input Data collected and spectrogram computed by H.L. Fournier Note frequency dependence on of decay time.

13. Example Given 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')

14. Room Modes The 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.

15. Example Generate 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.

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