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It is also possible to simply derive the relationship between the sound level in the room and the averaged sound power level of the musical instruments. The exercise will produce the formula (4) where the asterisk indicates the average vol- ume for performer, Tp is the empty room reverberation time and A; are the absorption units of a single musician which can be set at a value close to 0.7 m*. Despite its simplicity Eq. (4) highlights the main points that clearly regulate the sound level in the room as a design criteria. Typical trends of Eq. (3) are reproduced in Fig. 2. The atten- tion is focused on a realistic interval of reverberation times ranging from 0.6 s to 1.4 s and a set of curves is traced corre- sponding to combinations of room volume and heights. These parameters are also chosen in a suitable range usually found in rooms hosting a symphonic orchestra. As expected the dependence of ST 4,1. on reverberation time is very similar for all of the rooms and spans over a range of about +2.5 / +3 dB from shorter to longer reverberation.

Figure 2 It is also possible to simply derive the relationship between the sound level in the room and the averaged sound power level of the musical instruments. The exercise will produce the formula (4) where the asterisk indicates the average vol- ume for performer, Tp is the empty room reverberation time and A; are the absorption units of a single musician which can be set at a value close to 0.7 m*. Despite its simplicity Eq. (4) highlights the main points that clearly regulate the sound level in the room as a design criteria. Typical trends of Eq. (3) are reproduced in Fig. 2. The atten- tion is focused on a realistic interval of reverberation times ranging from 0.6 s to 1.4 s and a set of curves is traced corre- sponding to combinations of room volume and heights. These parameters are also chosen in a suitable range usually found in rooms hosting a symphonic orchestra. As expected the dependence of ST 4,1. on reverberation time is very similar for all of the rooms and spans over a range of about +2.5 / +3 dB from shorter to longer reverberation.

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The preliminary design steps can be taken over with the help of formulas derived by the so called revised theory applied to the definition of the parameters Early and Late Support de- fined in [5]. Unfortunately the simple equations (1) and (2) have the limit of not taking into account any geometrical contribution to the energetic ratio defining the support parameter. As a result they proved to underestimate the support by a few dBs.
The preliminary design steps can be taken over with the help of formulas derived by the so called revised theory applied to the definition of the parameters Early and Late Support de- fined in [5]. Unfortunately the simple equations (1) and (2) have the limit of not taking into account any geometrical contribution to the energetic ratio defining the support parameter. As a result they proved to underestimate the support by a few dBs.
Figure 1. The geometry of floor and ceiling reflections. Both surfaces are assumed sound reflecting. For this reason a more realistic tool can be developed by isolating the two outstanding first reflections of the reflective floor and ceiling which give an important energetic contribu- tion to the denominator and numerator of the support ratio respectively. Fig. 1 depicts the geometry of this simple sys- tem for a room of height H.
Figure 1. The geometry of floor and ceiling reflections. Both surfaces are assumed sound reflecting. For this reason a more realistic tool can be developed by isolating the two outstanding first reflections of the reflective floor and ceiling which give an important energetic contribu- tion to the denominator and numerator of the support ratio respectively. Fig. 1 depicts the geometry of this simple sys- tem for a room of height H.
The integral in the numerator of the support will be split in a first geometric contribution traced back to the ceiling and the statistical decay will start shortly after that: this is the reason why in the first exponential of Eq. 3 one finds the term r,. On the other hand the denominator will include direct sound at 1 m and the reflection at rp.
The integral in the numerator of the support will be split in a first geometric contribution traced back to the ceiling and the statistical decay will start shortly after that: this is the reason why in the first exponential of Eq. 3 one finds the term r,. On the other hand the denominator will include direct sound at 1 m and the reflection at rp.
Figure 2. A design chart for ST¢,,,, depending on rev. time expressed as function of room height and volume (in [m] and [10° m3] respectively).
Figure 2. A design chart for ST¢,,,, depending on rev. time expressed as function of room height and volume (in [m] and [10° m3] respectively).
‘igure 3. A design chart for the sound level as function of volume for performer V* and reverberation time Ty (A; = 0.7 m’). Another tool in the early design stages is the chart represent- ing the typical values of Eq. (4) shown in Fig. 3. In order to be effective the chart must be supplemented by the informa- tion on the averaged sound power level of each performer. This value Ly* clearly depends on the type of repertoire and on the orchestra composition. By referring to the data by [6] it can be hypothesized that for a theatre orchestra of 84 musi- cians including 64 strings, 8 woodwinds and 12 brass one has Ly*=95 dB when they play “forte’’.
‘igure 3. A design chart for the sound level as function of volume for performer V* and reverberation time Ty (A; = 0.7 m’). Another tool in the early design stages is the chart represent- ing the typical values of Eq. (4) shown in Fig. 3. In order to be effective the chart must be supplemented by the informa- tion on the averaged sound power level of each performer. This value Ly* clearly depends on the type of repertoire and on the orchestra composition. By referring to the data by [6] it can be hypothesized that for a theatre orchestra of 84 musi- cians including 64 strings, 8 woodwinds and 12 brass one has Ly*=95 dB when they play “forte’’.
Figure 4. A possible scheme for the disposition of the or- chestra in the rehearsal room.
Figure 4. A possible scheme for the disposition of the or- chestra in the rehearsal room.
Figure 5. Volume for performer V* as function of Number of performers (/V) for cell dimension (d) and height (H) (both in ml). CASE STUDIES
Figure 5. Volume for performer V* as function of Number of performers (/V) for cell dimension (d) and height (H) (both in ml). CASE STUDIES
Figure 6. Data for rooms A and B (three phases of acoustical design). Volume in [m*] and height in [m]. In the case of the room B the match is not as good though the trend in the points at the different reverberation values ap- pears to follow the overall course of the theoretical curve. In this case the room has reflectors instead of a proper ceiling in B-2 and B-3, and a non negligible contribution from lateral reflections is probably to be expected due to the nature of the lateral walls.
Figure 6. Data for rooms A and B (three phases of acoustical design). Volume in [m*] and height in [m]. In the case of the room B the match is not as good though the trend in the points at the different reverberation values ap- pears to follow the overall course of the theoretical curve. In this case the room has reflectors instead of a proper ceiling in B-2 and B-3, and a non negligible contribution from lateral reflections is probably to be expected due to the nature of the lateral walls.
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Mechanical EngineeringAcousticsClassical Physics
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