**8. Predictions, stochastic based simulations and measurements in the sample multimedia room**

220 Stochastic Modeling and Control

environmental noise level.

proper accuracy.

**a classroom** 

**7. Predicting measures for checking acquired acoustic quality in** 

**Figure 4.** Graphical layout for direct reading of reverberation time using a protractor

Based on the Schroeder integration, a special way of measuring reverberation time from the impulse response possible to implement into a digital sound measuring device was developed (e.g. B&K 2231 using a module for measuring reverberation time BZ 7108). The results are directly read from the instrument according to the octal and terca (tertiary bands) within the set frequency area. Reverberation time is calculated (extrapolation) based on 10, 20 and 30 dB of lowering of the signal level and thus avoiding the need for a 60 dB signal dynamics. The digital sound measurer or SPL meter (B&K 2231 using a module for measuring reverberation time BZ 7108), depending on the environmental noise level, itself generates the required signal level sufficient for measuring, based on the signal received with appropriate indicators of a low level or pre–actuation, independently carries out level correction. Due to the lowered influences of possible mistakes in measurement, four subsequent measurements within the entire frequency area, whose results are stored in digital sound measuring device memory and through statistical analysis can yield results of

The basic measurement of acoustic quality of a room is the measurement of reverberation time as the most important objective parameter of the acoustic quality of a room since it contains characteristics of a room such as dimension and volume and shape and absorption. Measuring reverberation time can be carried out in various ways and different types of measuring signals and sources of signal measurement are used. Basically, all types of measurement of reverberation time differ according to the principle of big difficulties created by the level of sound pressure of 60 dB above the noise level of the area which is needed according to definition for establishing reverberation time. The oldest way of measuring reverberation time is using the burst (pistol or similar) or noise (noise generator) which through frequency analyzer and logarithmic printer give a curve-like lowering of the sound pressure in a space. The Figure 4 graph shows the reverberation time measuring a protractor – a transparent board with scales for reading the reverberation time. In this type of measurement it is advisable that the level of actuation signal is at least 40-50 dB above The task is to make a prediction, stochastic based simulations and measurements of (some objective parameters of) acoustic (quality) in a sample multimedia classroom (classroom at the Department of Electroacoustics, Faculty of Electrical Engineering and Computing, or FER). Measurements and simulations of some objective parameters of acoustic quality in order to establish opinion whether the sample multimedia classroom is acoustic (according to some rules and conditions) or not, and if not, what measures should be taken in order for that classroom to meet the condition of acoustics. If the same measuring conditions are ensured, objective parameters of must be repeatable and be direct indicators of acoustic quality. The first measurable parameter is the reverberation time (time necessary for level of sound pressure or sound strength is lowered for 60 dB as sound emission is stopped).

Figure 5 shows the layout of the sample multimedia classroom. The numbers refer to positions in the room where reverberation time was measured, and the sound source is also marked with a symbol. Table 3 shows the results of the measurement of reverberation time depending on various frequencies of sound source in the real system.



The second measurable parameter is the distribution (division of the sound pressure). Sound pressure at a point in the room area is the result of the interference of direct and reflected sound and therefore in the spatial allocation of the sound pressure there are areas of minimum and maximum of sound pressure which are especially expressed in resonant frequencies. This parameter was measured at various frequencies in 30 points defined with introduced coordinates, shown in Figure 6. The results are shown in Table 4.

> **Position 31.5 Hz 63 Hz 125 Hz**  (1,1) 63.5 80.0 77.5 (1,2) 64.5 82.0 81.0 (1,3) 64.5 82.5 66.0 (1,4) 64.0 80.5 79.0 (1,5) 64.0 78.0 83.0 (2,1) 63.0 71.0 78.0 (2,2) 63.0 74.0 74.0 (2,3) 62.0 78.0 73.0 (2,4) 61.0 79.0 75.0 (2,5) 58.0 77.5 79.0 (3,1) 63.0 79.0 74.5 (3,2) 61.0 74.0 72.0 (3,3) 58.0 65.0 71.0 (3,4) 54.0 74.5 74.0 (3,5) 51.0 76.0 73.0 (4,1) 63.5 83.5 70.5 (4,2) 53.0 78.5 74.5 (4,3) 49.0 74.0 76.0 (4,4) 52.0 75.0 73.0 (4,5) 61.5 76.5 70.0 (5,1) 67.0 84.5 70.0 (5,2) 62.0 79.5 73.0 (5,3) 64.0 75.5 74.0 (5,4) 68.0 77.5 73.0 (5,5) 67.0 77.0 73.0 (6,1) 65.5 80.0 71.0 (6,2) 58.5 79.5 62.0 (6,3) 56.5 77.5 70.0 (6,4) 65.0 79.0 75.5 (6,5) 68.5 83.0 77.0

**Table 4.** Level of sound pressure in dB for particular frequencies

analyzer.

The obtained results for sound level in decibel (dB) are relative, considering that they are only relevant for differences in levels for particular frequencies. Separate measurement was conducted using Bruel and Kjaer sound measuring device (SPL meter - B&K 2231 using a module for measuring reverberation time BZ 7108) which was attached to a spectral

Measurement was conducted in the spot which is marked by number 1 on Figure 7 and the shaded area around that place. The speakers emitted a white murmur and the spectral analyzer recorded the situation for several spots in the area. The results were transferred

**Figure 5.** Room layout CX-15 (sample multimedia room)

**Figure 6.** Measurement of sound pressure distribution


**Table 4.** Level of sound pressure in dB for particular frequencies

222 Stochastic Modeling and Control

**Figure 5.** Room layout CX-15 (sample multimedia room)

**Figure 6.** Measurement of sound pressure distribution

The obtained results for sound level in decibel (dB) are relative, considering that they are only relevant for differences in levels for particular frequencies. Separate measurement was conducted using Bruel and Kjaer sound measuring device (SPL meter - B&K 2231 using a module for measuring reverberation time BZ 7108) which was attached to a spectral analyzer.

Measurement was conducted in the spot which is marked by number 1 on Figure 7 and the shaded area around that place. The speakers emitted a white murmur and the spectral analyzer recorded the situation for several spots in the area. The results were transferred

into the program Matlab which created a graph shown in Figure 8. Figure 8 shows the dependency of the sound pressure on frequency in spot 1. The results of the measurement in

Figure 8 shows resonances, that is, points which represent standing waves maximum. The most prominent maxima are at the frequency of about 26 Hz, followed by 50 Hz and 75 Hz.

The measure represents the speed of sound in the air which is c= 340 m/s, A, B and C are room dimensions, and p, q and r are natural, whole numbers. Room dimensions: A=6.7 m;

Table 5 gives the results of the calculation of resonant frequencies and it is evident that the calculated values coincide with the measured values. The most prominent frequencies are 26

The following step was the acoustic simulation on the computer. For that purpose the EASE program (version 4.1) was used. The aim of the simulation was to show the reverberation time at various frequencies depending on the construction materials used. For calculating reverberation time, the Eyring formula was used and set with the following expression:

2 2 2 <sup>222</sup> 2 *c r p q <sup>f</sup> <sup>A</sup> B C* 

the area are rather similar to the results of measurement in that spot.

Such maxima show up at resonant frequencies obtained by the formula:

B=7.2 m; C=3.2 m.

**Table 5.** Resonant frequency calculation results

and 74 Hz.

**Figure 7.** The measurement was carried out in the area marked with number 1 and the shaded area around that spot

**Figure 8.** Measured resonances (points which represent maximum standing waves)

into the program Matlab which created a graph shown in Figure 8. Figure 8 shows the dependency of the sound pressure on frequency in spot 1. The results of the measurement in the area are rather similar to the results of measurement in that spot.

Figure 8 shows resonances, that is, points which represent standing waves maximum. The most prominent maxima are at the frequency of about 26 Hz, followed by 50 Hz and 75 Hz. Such maxima show up at resonant frequencies obtained by the formula:

$$f = \frac{c}{2} \sqrt{\frac{p^2}{A^2} + \frac{q^2}{B^2} + \frac{r^2}{C^2}}$$

The measure represents the speed of sound in the air which is c= 340 m/s, A, B and C are room dimensions, and p, q and r are natural, whole numbers. Room dimensions: A=6.7 m; B=7.2 m; C=3.2 m.

Table 5 gives the results of the calculation of resonant frequencies and it is evident that the calculated values coincide with the measured values. The most prominent frequencies are 26 and 74 Hz.


**Table 5.** Resonant frequency calculation results

224 Stochastic Modeling and Control

around that spot

**Figure 7.** The measurement was carried out in the area marked with number 1 and the shaded area

**Figure 8.** Measured resonances (points which represent maximum standing waves)

The following step was the acoustic simulation on the computer. For that purpose the EASE program (version 4.1) was used. The aim of the simulation was to show the reverberation time at various frequencies depending on the construction materials used. For calculating reverberation time, the Eyring formula was used and set with the following expression:

$$T\_r = \frac{0.161V}{-S\ln(1-a)}$$

Therefore, the back wall should be entirely covered with absorbing diffuser whose

dependency of absorbency coefficient on frequency is shown in Figure 11.

**Figure 11.** Overview of the dependency of absorbency coefficient on frequency

**Figure 10.** Second simulation results

Where V is room volume, S is the sum of all areas in the room, and average absorption coefficient. The simulation of the current situation of the room was conducted first. The simulation results are presented in Figure 9, which shows that the situation is not satisfactory for frequencies lower than 2 kHz, considering that there is a large deviation in the reverberation time from normal values. Because of that some changes were necessary. In the area (virtual, used in the simulation) absorbers, materials used for "absorbing" sound waves, were used. To be more exact, they were placed on the only available wall in the room.

**Figure 9.** Results of the first simulation

After that, another simulation took place, the results of which are shown in Figure 10. As it can be seen on Figure 10, the results are rather satisfactory considering that there are no great deviations in the reverberation time from optimal values.

**Figure 10.** Second simulation results

226 Stochastic Modeling and Control

**Figure 9.** Results of the first simulation

room.

0.161 ln(1 ) *<sup>r</sup> <sup>V</sup> <sup>T</sup> S*

Where V is room volume, S is the sum of all areas in the room, and average absorption coefficient. The simulation of the current situation of the room was conducted first. The simulation results are presented in Figure 9, which shows that the situation is not satisfactory for frequencies lower than 2 kHz, considering that there is a large deviation in the reverberation time from normal values. Because of that some changes were necessary. In the area (virtual, used in the simulation) absorbers, materials used for "absorbing" sound waves, were used. To be more exact, they were placed on the only available wall in the

After that, another simulation took place, the results of which are shown in Figure 10. As it can be seen on Figure 10, the results are rather satisfactory considering that there are no

great deviations in the reverberation time from optimal values.

Therefore, the back wall should be entirely covered with absorbing diffuser whose dependency of absorbency coefficient on frequency is shown in Figure 11.


**Figure 11.** Overview of the dependency of absorbency coefficient on frequency

#### 228 Stochastic Modeling and Control

It is important to mention how in acoustic room simulation, some additional objects such as cupboards, board, etc. were not taken into consideration since they have a marginal influence on the end results constraint.

Stochastic Based Simulations and Measurements of Some Objective Parameters of Acoustic Quality: Subjective Evaluation of Room Acoustic Quality with Acoustics Optimization in Multimedia Classroom … 229

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