14 Phonetogram data, perceptual voice quality, subjective ratings, and gender differences in
V. DISCUSSION
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.
0 5 10 15
−5 0 5 10
Distance [m]
G [dB]
Gdir
Small
0 5 10 15
−5 0 5 10
Distance [m]
G [dB]
Medium
0 5 10 15
−5 0 5 10
Distance [m]
G [dB]
Large
FIG. 4. Measurements of sound strength due to direct sound (Gdir), early reflections (Ger), and late reflections (Glate), as a function of the distance to the source. The regression lines for the two latter components are shown. Left: small rooms.
Middle: medium rooms. Right: large rooms.
TABLE VII. Frequency band values and overall speech-weighted voice support (STV) and room gain (GRG) measured in the classrooms.
Speech-Octave band center frequency (Hz) 125 250 500 1000 2000 4000 weighted
Small classrooms
Mean STV (dB) -9.4 -11.1 -9.5 -7.6 -6.4 -4.6 -8.3
s.d. 0.46 0.81 0.91 0.38 0.72 1.04 0.50
Mean GRG(dB) 0.50 0.33 0.47 0.70 0.91 1.31 0.60
s.d. 0.02 0.06 0.09 0.06 0.13 0.25 0.07
Medium classrooms
Mean STV (dB) -12.1 -13.9 -13.5 -11.6 -10.9 -9.1 -12.2
s.d. 1.46 1.27 1.43 1.68 1.75 1.52 1.43
Mean GRG(dB) 0.28 0.18 0.20 0.32 0.37 0.54 0.26
s.d. 0.10 0.06 0.07 0.13 0.16 0.19 0.09
Large classrooms
Mean STV (dB) -10.8 -16.0 -18.2 -19.1 -19.5 -19.4 -17.9
s.d. 1.56 1.91 0.92 1.31 1.40 1.31 0.51
Mean GRG(dB) 0.36 0.12 0.07 0.06 0.05 0.06 0.07
s.d. 0.14 0.06 0.01 0.02 0.02 0.02 0.01
−20 −15 −10 −5
−25
−20
−15
−10
−5
Expected STV [dB]
Measured STV [dB]
125 Hz y = 0.97x − 3.2
R2 = 0.18
σε = 3.3 dB σT = 4.3 dB
−20 −15 −10 −5
−25
−20
−15
−10
−5
Expected STV [dB]
Measured STV [dB]
250 Hz y = 1.4x + 3.9
R2 = 0.63
σε = 1.8 dB σT = 2.9 dB
−20 −15 −10 −5
−25
−20
−15
−10
−5
Expected STV [dB]
Measured STV [dB]
500 Hz y = 0.98x − 0.17
R2 = 0.81
σε = 1.1 dB σT = 1.1 dB
−20 −15 −10 −5
−25
−20
−15
−10
−5
Expected STV [dB]
Measured ST V [dB]
1 kHz y = 0.79x − 3.5
R2 = 0.8
σε = 1.2 dB σT = 1.7 dB
−20 −15 −10 −5
−25
−20
−15
−10
−5
Expected STV [dB]
Measured ST V [dB]
2 kHz y = 0.83x − 2.2
R2 = 0.84
σε = 1.2 dB σT = 1.4 dB
−20 −15 −10 −5
−25
−20
−15
−10
−5
Expected STV [dB]
Measured ST V [dB]
4 kHz y = 0.8x − 0.031
R2 = 0.83
σε = 1.4 dB σT = 2.4 dB
FIG. 5. Expected versus measured values of voice support in frequency bands. The solid lines show the regression lines for the predictions and the dotted lines indicate the ideal and unbiased prediction lines.
9
−20 −15 −10
−22
−20
−18
−16
−14
−12
Speech weighted Expected STV
Measured ST V [dB]
FIG. 6. Expected versus measured speech-weighted overall values of voice support. The solid lines show the regression lines for the predictions and the dotted lines indicate the ideal and unbiased prediction lines.
The values of Grefl,dif are shown as solid lines in Fig. 7 for each of the 3 classroom groups. The quantities V and S were derived from the average dimensions in Table II, assuming a box geometry, which is the case for nearly every room. V and S were 41 m3 and 72 m2 for small classrooms, 180 m3 and 218 m2 for medium-sized class-rooms, and 3614 m3 and 1640 m2 for large classrooms.
The values used for T are the ones on Table V: 0.33 s for small classrooms, 0.46 s for medium classrooms, and 1.57 s for large classrooms.
According to the revised theory of Barron and Lee,35 the reflected energy (early+late) at the source position is equal to the energy predicted by the diffuse field the-ory and decays exponentially with the distance from the source according to
Grefl,BL= 10 log 31220T
V −5026 S
e−0.04dT
. (30) The predictions for Grefl,BL according to Barron and Lee’s theory for each group of classrooms are shown as dashed lines in Fig. 7. The slopes of these lines are -0.53 dB/m for small classrooms, -0.38 dB/m for midsize classrooms, and -0.11 dB/m for large classrooms. These values are approximately one half of the slopes from the regression lines in Eq. (27). This result is in good agree-ment with the findings of Sato and Bradley,24who found that the experimental decrease of the level of the early re-flected sound was twice as derived by Barron and Lee.35 The sound strength of the reflected sound, Grefl,meas ob-tained by the combination of the regression lines for the early reflected sound in Eq. (27) and the late reflected sound in Eq. (28) through Eq. (24) are shown as dash-dot curves in Fig. 7. This figure shows that Glate has an influence on Grefl,meas only at long distances. Therefore, the average deviation of Grefl,measfrom Grefl,BLare lower than considering a linear decay of Glateaccording to Sato and Bradley.
An important observation from Fig. 7 is that Grefl,meas
matches the predictions from the diffuse field theory at the source position, and also Barron and Lee’s prediction,
According to the measurements, Glate is nearly uni-form across the room. This is yet another indication that the late part of an impulse response has statistical properties related to the room and not to the placement of source and receiver. The early and the late reflections have been separated as those arriving before and after 50 ms from the arrival of the direct sound, respectively.
However, the present results suggest that the transition time between early and late reflections could be defined as the minimum time in the impulse response after the ar-rival of the direct sound for which the statistics of the late reflections are independent of the position in the room.
The prediction model for STV has been derived theo-retically and it has been assessed by comparing its pre-dictions with actual STV measurements. There is a bias in the prediction, as the regression line of measured versus predicted STV is not STV,pred = STV,meas but STV,pred = 0.95 · STV,meas− 1.4 (see Fig. 6). This bias results in a deviation of 1.4 dB from the actual values, slightly higher than the residual deviation (1.1 dB). Tak-ing into account that the measurement dataset has not been used to derive the model, the predictions are rea-sonably accurate.
In the range of medium-sized classrooms (with volumes 100 < V < 250 m3), GRGis in the range between 0.2 and 0.5 dB, whereas STV is in the range between 14 and -9 dB. There is some spread of data in this range, as seen in Fig. 6. Measured STV values can deviate as much as 3 dB from the predicted value. STV is influenced by the early reflections which can not be accurately represented with a statistical model such as the one in Eq. (18).
The voice support, analogously to the objective sup-port in concert halls, is not a stand-alone parameter to design classroom acoustics. It is a magnitude related to the additional vocal load that teachers experience while speaking in a classroom due to the acoustic conditions.
Other magnitudes, like T , G, STI, and background noise levels should be taken into account as well. There is not enough scientific evidence to establish a definite range of recommended values of STV, but the range between -14 and -9 dB obtained in most of the medium-sized class-rooms seems adequate, since T and STI fulfilled the rec-ommendations without the rooms being too damped. Us-ing the graph in Fig. 2, for a room of 100 m3, the range of −14 < STV < −9 dB corresponds to reverberation times in the range 0.25 < T < 0.6 s. For a room of 300 m3, the same range of STV corresponds to the range 0.55 < T < 1.4 s. In this last case, the design criteria should be to aim at the highest reverberation time that does not compromise speech intelligibility, because too high values of reverberation are detrimental to speech intelligibility. For the same reason, it is not adviceable to aim at values of STV higher than -9 dB. However, in very small classrooms, STV may be higher than -9 dB without compromising speech intelligibility.
10
0 5 10 15
−5 0 5 10
Distance [m]
G [dB]
Small
Gdir
Grefl,meas
0 5 10 15
−5 0 5 10
Distance [m]
G [dB]
Medium
0 5 10 15
−5 0 5 10
Distance [m]
G [dB]
Large
FIG. 7. Predicted sound strength as a function of the distance to the source for the direct and reflected components, according to the diffuse-field theory (Grefl,dif, solid line), Barron and Lee’s revised theory (Grefl,BL, dashed line), and the combination of the regression lines on Eqs. (27) and (28) (Grefl,meas, dash-dot line). Left: small rooms. Middle: medium rooms. Right: large rooms.