In the previous lesson, we showed that the relationship between acoustic power level and room sound pressure level can be expressed as equation (1) using the room constant R and the distance r from the sound source, and we derived approximate equations for free sound fields such as anechoic chambers and diffuse sound fields in spaces with long reverberation.
..................................................................（1）
Lp: Sound pressure level Lp at a point at a distance r from the sound source.
L w: Sound power level of the sound source
..................................................................（2
R: Room constant
S: Total interior surface area
α: Average sound absorption coefficient
T: Room reverberation time
V: Chamber volume
This time, we will show the process of using this formula to determine the sound pressure level at a specific point in a room. In formula (1), even if Lw is unknown, if the room constant R is known, the difference in sound pressure levels between two points at a certain distance from the sound source can be determined. As shown last time, R is calculated using formula (2), so it is necessary to determine the average sound absorption coefficient of the room, and for that, it is necessary to measure the reverberation time.
Here, we tried calculating how much the sound pressure level changes with distance from the sound source by giving R a range of values and removing Lw from equation (1). The result is shown in the graph in Figure 1 on the next page. The case where R is infinite corresponds to a free sound field, and we get equation (3) shown last time, which is a curve in which the sound attenuation decreases by 6 dB for every doubling of the distance r.
.................................（3）
This is what is known as distance attenuation. Also, as R decreases, the amount of attenuation decreases, but you can see that the smaller R is, the closer you are to the sound source, and the more constant the sound pressure level becomes.
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Figure 1
As this graph shows, even if R doubles, the difference in sound pressure level is at most about 3 dB. As mentioned earlier, measuring the reverberation time is necessary to precisely determine R, but even a rough understanding of R is sufficient to grasp the tendency of attenuation. It is possible to estimate R by calculating the average sound absorption coefficient α from the sound absorption coefficient αi of the materials that make up the room (the sound absorption coefficients of various interior materials can be obtained from related books and material catalogs), as shown below.
S: Total interior surface area
A: Equivalent sound absorption area of the room
Si: Surface area of each interior material
A j: Equivalent sound absorption area of the individual
Let's consider the case of two identical rectangular rooms with different sound absorption properties, as shown below.
One case involves having measured reverberation time, and the other involves having the sound absorption coefficient (catalog data) of the interior materials that make up the room.
Conditions: Rectangular room with a volume of 1440 m³ (12 m wide x 15 m deep x 8 m high), surface area of the room: 792 m²
① Assume the measured reverberation time is 2.6 s.
Based on K = 0.161 and V = 1440 (room volume),
② Assume the sound absorption coefficients of the interior materials are: walls = 0.65, floors = 0.1, and ceilings = 0.80.
Average sound absorption coefficient
Room ① has an average sound absorption coefficient of slightly over 10%, making it a lively space with considerable reverberation. Room ②, when its reverberation time is calculated, is T = KV / Sα = 0.161 × 1440 / (792 × 0.56) = 0.52 s, which is about 1/5 the reverberation time of room ①, making it a dead space with high sound absorption as an indoor space. In terms of R, room ② is about 10 times that of room ①. The relative sound pressure level differences at 1m, 5m, 10m, and 20m are shown in Table 1 below.
Table 1: Relative sound pressure levels of sound fields ① and ②, and free sound field
| Distance from sound source (m) | ① | ② | free space |
| 1 | -9.2 | -10.8 | -11 |
| 2 | -12.2 | -16.2 | -17 |
| 5 | -13.6 | -21.4 | -25 |
| 10 | -13.9 | -21.4 | -31 |
If Lw is known, adding Lw to the values in the table above will give you the sound pressure level at that location. Conversely, if the room constant can be calculated from the measured reverberation time and interior material data as described above, and the sound pressure distribution in the room can be measured, it is possible to calculate the acoustic power level Lw. However, if the room's diffusivity is insufficient, for example, if sound-absorbing materials are unevenly distributed or if there are reflective objects close to the sound source and receiving point, the equation (1) assuming a diffuse sound field may not be satisfied, and it is best to use it only as a rough guideline to get a general idea of the value.
(Excerpt from the email newsletter issued on April 22, 2010)
