Last time, we used the relationship between sound power level and room sound pressure level to specifically describe a point in a room.
I showed the process for determining the sound pressure. As mentioned at the end, if sound-absorbing material is unevenly distributed,
If there are reflective objects near the sound source and the point of reception, the diffuse sound field condition is not satisfied, and the presented equation is not valid.
This will result in a difference from the previous outcome.
Furthermore, in the case of a rectangular prism-shaped room, even if the room surface is rigid, the dimensions are determined by the ratio of depth, width, and height.
At the natural vibration frequency of the room, if there are pure tone components close to that frequency, standing waves will be generated in the room.
The diffuse properties of the sound break down, and the calculation formula based on the assumption of a diffuse sound field, as shown previously, no longer holds true.
This time, we will calculate the relationship between the dimensional ratio of a room and its natural frequency using two rooms of different scales as examples.
I'll take a look.
The natural vibration frequency of a rectangular chamber is expressed as follows:
.................................(1)
Here, since there is an inherent frequency for any combination of nx, ny, and nz, the number of such combinations is infinite, but they can be classified into three types based on the combination.
- 1D mode (axial mode)
A wave in which two of nx, ny, and nz are zero. Since it is a wave parallel to a single axis, it is called an axial wave.
Masu. - 2D mode (tangential mode)
One of the three n values is 0. Parallel to one pair of parallel walls, and on the other two pairs of walls.
A wave that is incident at an oblique angle is called a tangential wave. - 3D mode (oblique mode)
These are waves where all three values of n are not zero. All waves are incident at an oblique angle and are called oblique waves.
Table 1 Two rectangular chambers used in the calculations (units: m)
| Width | Depth | Height | Expected rooms | |
| Rectangular Room A |
2.0 |
3.0 |
1.5 |
A room about the size of the inside of a car. |
| Rectangular prism room B |
8.0 |
11.0 |
5.0 |
A small hall that can accommodate about 50 people |
Using the two rooms shown in Table 1 as an example, the estimated natural vibration frequencies show the distribution shown in Figure 2 on the next page.
Rectangular room A is a room designed to be about the size of a car interior, but below 100Hz there are only two natural frequencies, both of which are axial waves in the first mode, with the lowest frequency being 57Hz and the other being 85Hz. Because the dimension ratio of depth to height is 2:1 and the dimension ratio of depth to width is 3:2, the frequencies that coincide, such as no. 7 and no. 8, and no. 11 and no. 12, which are shown in the low-to-high natural vibration frequencies in Figure 2, occur frequently. In interior design, it is desirable to disperse natural vibration frequencies as much as possible, and the design of a room composed of such simple dimension ratios should be avoided.
Rectangular Room B is a room envisioned as a small hall accommodating about 50 people, but it is approximately 50 times larger in volume and 3.7 times larger in dimensions compared to Rectangular Room A. The lowest natural vibration frequency is 15 Hz, and there are 66 natural frequencies below 100 Hz. (The 50th natural frequency on the list is 86 Hz.) There are four combinations of 71 Hz from no. 29 to no. 32. Natural vibrations also exist at adjacent frequencies before and after, and it can be estimated that the frequency distribution centered around 71 Hz is a frequency at which resonance and anti-resonance are likely to occur depending on the location.
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Figure 2. Natural vibration frequencies of the two rooms (the list shows the 50 lowest frequencies).
Thus, when designing a room based on a rectangular prism, considering dimensional ratios that prevent concentration in the distribution of natural vibration frequencies is an important factor, along with design considerations such as reverberation time.
Furthermore, the natural vibration frequency of a room is typically measured by sweeping a pure tone, which then represents the transmission frequency characteristics within the room.
(Excerpt from the email newsletter issued on May 20, 2010)
