RESULTS

A. Correlation between parameters

The correlation coefficients between the measurements of the magnitudes V , log(V ), L_N,Aeq, T_500−2k, G_500−2k, STI, G_RG, and ST_V are shown in Table III. L_N,Aeq has

5

+ +

-+

+

-+

FIG. 3. Block diagram of the post-processing applied to the the impulse responses to extract the sound strength of early and late reflections

very low correlation with all the other parameters, be-cause it is not determined from physical properties of the room, but depends on different noise sources from installations inside the room, and from other external noise sources (traffic noise, students in neighboring class-rooms, corridors, or playground). The reverberation time is correlated to the volume and negatively correlated to the STI. The voice support is strongly correlated to the logarithm of the volume, as expected from the predic-tion model in Eq. (18), and to the sound strength. Both parameters are descriptors of the amplification of sound due to reflections. The presence of some high correla-tion coefficients is largely caused by the large measured range of volume and most of the other parameters of the classrooms.

B. Background noise levels

The mean and maximum background noise levels (A-weighted and in one octave frequency bands) are shown in Table IV. Although it is not explicitly shown, 73.3%

of the classrooms had LN,Aeqlower than 35 dB, another 13.3% between 35 and 40 dB, and the remaining 13.3%

of the measurements were between 40 and 45 dB. In most of the cases, the noise sources corresponded to the venti-lation systems, although in a few cases, the background noise was affected by external sources, such as neighbor-ing activities, playground, and traffic. The background noise levels were similar for all room sizes, although the overall level in the large rooms was slightly higher than in smaller rooms. In all cases, low frequency noise was markedly dominating. This is an indication that the sources, in most of the cases, were in fact machinery of the ventilation systems, or external noise that breaks in the room due to the usually low insulation performance of walls, doors, and windows at low frequencies.

C. Reverberation time

The mean reverberation times (in one octave frequency bands and 500 Hz-2 kHz average) and their standard de-viation are shown in Table V. 81.5% (22 out of 27) of the small and medium classrooms had reverberation times lower than 0.5 s, and the remaining 18.5% were between 0.5 and 0.6 s. In the sports halls, T was between 1.4 s and 1.8 s.

D. Speech transmission index

The average (standard deviation) measured STI was 0.80 (0.02) in small classrooms, 0.75 (0.03) in medium classrooms and 0.63 (0.02) in large classrooms. The spread of STI among rooms, indicated by the stan-dard deviation, was similar in all of the three classroom groups. The small classrooms had the highest STI, which falls in the category of ’excellent’. The medium class-rooms had an average STI rating which is between ’good’

and ’excellent’, and the sports halls had an STI rating of

’good’ which is likely to decrease in the presence of ac-tivity noise.

E. Sound strength

The numerical values of the mean and standard de-viation of G among different classroom groups, in one octave bands from 125 Hz to 4 kHz, along with the av-erage on the 500 Hz, 1 kHz, and 2 kHz bands, are shown in Table VI. G depends on the volume and it has high-est values for the smallhigh-est rooms. There are two factors contributing to the increased G values. First, the en-ergy density increases as the volume decreases and, sec-ond, the students are closer to the teacher than in larger rooms, receiving an important contribution from the di-rect sound. The spread of G among rooms, indicated by the standard deviation, does not show any clear

depen-6

log V 1.00 0.27 0.91 -0.57 -0.75 -0.87 -0.90

LN,Aeq 1.00 0.24 -0.14 -0.10 -0.19 -0.27

T500−2k 1.00 -0.89 -0.47 -0.70 -0.74

STI 1.00 0.55 0.68 0.68

GRG 1.00 0.94 0.81

STV 1.00 0.89

G500−2k 1.00

TABLE IV. Frequency band values and overall A-weighted background noise levels (BNL) measured in the classrooms.

Octave band center frequency (Hz) 125 250 500 1000 2000 4000 A-weighted

Small classrooms

Mean BNL (dB) 38.3 32.4 28.2 26.1 22.3 19.4 32.3

Maximum BNL (dB) 48.8 39.3 34.5 32.6 27.5 21.3 38.5

Medium classrooms

Mean BNL (dB) 40.2 33.7 27.8 24.4 22.7 19.9 32.7

Maximum BNL (dB) 53.4 43.6 43.7 40.1 37.3 32.4 43.5

Large classrooms

Mean BNL (dB) 45.1 37.9 33.5 32.0 28.3 21.9 37.6

Maximum BNL (dB) 51.5 46.2 41.1 37.4 30.1 23.2 43.5

dence on the frequency.

It is important to know G at different positions in class-rooms to calculate the level of the speech signal and pre-dict speech intelligibility in classrooms based on signal-to-noise ratios. The dependence of G with distance is hidden in Table VI. The contribution of Gdir, Ger, and G_lateto G at different distances in the 3 classroom groups is shown in Fig. 4. Regression lines were obtained for G_er and Glatein each group of classrooms. The corresponding equations (with dB units) are

Ger=







21.5 − 1.1d small (R²= 0.36; p = 0.11) 16.5 − 0.6d medium (R²= 0.18; p < 0.001) 7.9 − 0.3d large (R²= 0.61; p = 0.003)

(27)

G_late=







9.2 + 0.2d small (R²= 0.01; p = 0.79) 8.6 − 0.04d medium (R²= 4 · 10⁻⁴; p = 0.86) 5.9 − 0.02d large (R²= 0.02; p = 0.69)

(28) where d is the source-receiver distance. There is a large spread in the data, which is reflected in the low R² val-ues in the regression lines. However, the regression lines for Ger in medium and large classrooms are significant at the 5% level, and in small classrooms the p-value is 0.11, indicating a likely trend which could have been sig-nificant with a larger sample of measured classrooms. In all classroom sizes, Ger decreases with distance, and the slope is less steep the larger the room. The low R² val-ues and non-significant effects for the regression lines of G_late indicate that, most likely, G_late is uniform at the different positions in the room.

F. Voice support and room gain 1. Measurements

The mean and standard deviation of STV and GRG

in the one-octave frequency bands between 125 Hz and 4 kHz measured in the classrooms is shown in Table VII.

The frequency characteristics of STV and GRGare sim-ilar for small and medium classrooms, with a remark-able increase at high frequencies. The only difference be-tween the two classroom groups is that the small class-rooms have a slightly higher overall value. The large classrooms (sports halls) have an overall lower value and, in addition, the frequency characteristic is qualitatively different, because the low frequencies are predominant.

This indicates that these large rooms do not reflect ef-ficiently the high frequencies of a talker. The spread of STV among rooms does not depend on the frequency band, since the standard deviation does not present a frequency-dependent pattern in the different classroom groups. However, the standard deviation of GRGis pro-portional to its absolute value.

2. Prediction model

The values of V and S of each classroom, together with the frequency-dependent average measurements of T , were used in connection with Eq. (18) to predict the STV values. The comparison between the measured and the predicted values of STV in the one-octave frequency bands between 125 Hz and 4 kHz is shown in Fig. 5. The most accurate predictions are found in the most impor-tant bands for speech (between 500 Hz and 2 kHz). In

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Small classrooms

Mean T (s) 0.59 0.39 0.32 0.34 0.35 0.34 0.33

s.d. 0.42 0.14 0.04 0.05 0.05 0.02 0.05

Medium classrooms

Mean T (s) 0.72 0.53 0.45 0.47 0.47 0.44 0.46

s.d. 0.33 0.17 0.08 0.08 0.07 0.07 0.08

Large classrooms

Mean T (s) 1.46 1.58 1.59 1.55 1.35 1.04 1.57

s.d. 0.24 0.35 0.29 0.18 0.07 0.07 0.23

TABLE VI. Frequency band values and overall speech-weighted sound strength (G) measured in the classrooms averaged for four distances in each room.

Average

Octave band center frequency (Hz) 125 250 500 1000 2000 4000 500–2000

Small classrooms

Mean G (dB) 21.7 21.4 18.1 20.7 21.5 22.9 20.1

s.d. 3.6 2.0 0.8 1.1 1.3 1.4 1.1

Medium classrooms

Mean G (dB) 19.4 18.2 13.8 15.8 16.8 17.7 16.0

s.d. 2.6 2.1 1.9 1.5 1.6 1.7 1.6

Large classrooms

Mean G (dB) 13.4 12.9 6.8 8.8 9.2 8.9 9.4

s.d. 1.2 0.3 1.0 1.1 1.4 2.1 0.7

these bands, R² was at least 0.8, the residual deviation was not higher than 1.2 dB, and the bias or deviation from the unbiased prediction was lower than 2 dB. The prediction for the 125 Hz band had a large uncertainty, shown by the low value of R² (0.18), and large residual deviation (3.3 dB) and bias (4.3 dB).

The speech-weighted STV predictions are plotted in Fig. 6 as a function of the measured STV values. The re-gression line relating measurements and predictions had a slope of 0.95 (whereas ideally, it should be 1). The R² was 0.84, the residual error was 1.1 dB and the bias was 1.4 dB.