In the previous article, we discussed acoustic power level as a basic measure of sound emitted from a sound source. This time, we will discuss the basic relationship between acoustic power level and sound pressure level in a room. Knowing this relationship allows us to determine the acoustic power level by measuring the sound pressure level at a certain point, and then using the room's reverberation time, total surface area, and the distance between the sound source and the receiving point. Conversely, if the acoustic power level is known during the design phase, it is also possible to predict the sound pressure level at a certain point.
In indoor noise measurements, the noise level is evaluated by measuring the sound pressure at the problematic point, and the impact is sometimes understood by measuring near the source of the noise (for example, at a distance of 1 meter from the source). Before sound power levels were widely used, sound sources were also evaluated using values obtained from the above-mentioned measurements at the site. However, noise levels and sound pressure levels change depending on the acoustic environment of the location where the sound source is placed and the conditions of the measurement point (distance and direction from the sound source, etc.).
Measurement of sound source power levels, unaffected by environmental factors, is governed by standards, ranging from office equipment and IT devices to construction machinery. Please refer to the information below for details.
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Figure 1 shows a case where the sound source and the sound receiver are located in a closed space. This corresponds to a scenario where workers are exposed to noise while factory machinery is in operation.
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Figure 1
The sound pressure level at a given point in a room is contributed to by both direct sound transmitted directly from the sound source and diffuse sound, which is the sum of reflected sound reflected by the walls, floor, and ceiling of the room. Equation (1) below expresses the sound pressure level at a distance r from the sound source using the acoustic power level. This equation is derived from energy density, an important fundamental quantity in acoustics, which is the acoustic energy per unit volume generated by both direct and diffuse sound. However, the process is somewhat complex, so we will omit it here.
This formula is derived by assuming that after the direct sound is reflected once by a wall, it then diffuses uniformly as diffuse sound.
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、
.................................................................（1）
L p: Sound pressure level Lp at a point at a distance r from the sound source
L w: Audio power level of the sound source
S: total room surface area
α: Average sound absorption coefficient
R is the room constant;
..................................................................（2）
The average sound absorption coefficient α is calculated using the following formula by determining the reverberation time T of the room.
Here, in free space, α = 1, so R → ∞ (α = 1, perfect sound absorption), and the 4 / R term in equation (1) becomes 0;
.................................（3）
When the reverberation is long and α is small (the equivalent sound absorption area is small), R → A takes a value close to Sα, and 1 / 4πr² << 4 / R;
.................................（4）
Equation (3) is applicable to anechoic chambers, and equation (4) is applicable to reverberation chambers or spaces with long reverberation times, such as halls. In typical indoor spaces, equation (1) is used to find the relationship between sound power level and sound pressure level.
(Excerpt from the email newsletter issued on March 18, 2010)
