Starting with this installment, I'd like to cover the topic of "Reverberation Theory and Measurement of Reverberation Time" in several parts.
Reverberation time is the most fundamental quantity that describes the characteristics of the sound field in a room. It is an important physical quantity that is measured not only when directly indicating the reverberation of a room, but also when calculating the acoustic performance of materials, such as the sound absorption coefficient (reverberation room method sound absorption coefficient) and sound transmission loss (reverberation room-reverberation room method).
In the previous article, we showed how to determine the natural vibration frequency of a rectangular chamber. Depending on the dimensional ratio, there may be many cases where the natural vibrations overlap at the same frequency. This is called degeneracy, and it is an undesirable phenomenon in room acoustics. A sound field that does not exhibit such degeneracy, has a uniform distribution, and shows constant attenuation during the sound decay process, such as a reverberation chamber, is called a diffuse sound field. Reverberation theory is based on the premise of a diffuse sound field.
The definition of a diffuse sound field is,
- The acoustic energy density is uniform.
- The flow of acoustic energy is equally probable in all directions at all points.
This is a crucial prerequisite for developing reverberation theory. Acoustic energy was explained in the 11th lesson as follows.
Sound propagating through the air can be thought of as a flow of energy, and this energy is called acoustic energy. The quantity that represents this acoustic energy is the amount of acoustic energy passing through a certain surface per unit time, which is called "acoustic power" P (W)."Acoustic intensity" I (W/m2), or the strength of sound, can be described as the power passing through a unit area.
For a plane wave, the acoustic energy density is calculated as follows: the energy I (acoustic intensity) flowing per unit area per second exists over a distance c (m). Therefore, the energy density of sound in that space is E = I/c (W/ m³), where c is the speed of sound.
However, in the case of a diffuse sound field, acoustic energy propagates in all directions, so it is not as simple as with a plane wave. Let's use Figure 1 below to find the acoustic energy density in a diffuse sound field.
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Figure 1: Incidence from diffuse sound field to wall
Let E be the acoustic energy density in a diffuse sound field, and let E be a minute scale containing a point at a distance r from a portion of the wall dS.
Let ΔIdS be the energy that enters dS from the energy EdV contained in volume dV.
In Figure 1, the effective area of dS as seen from dV is dS cosθ, so
.................................(1)
Therefore, the total energy Ei incident on dS in one second is the amount of sound that propagates around dS in one second.
We find this by integrating it for all dV within the radius of the distance c.
If the polar coordinates of dV centered at dS are r, θ, and ψ, then
.................................(2)
As a result, the amount of acoustic energy incident per second on a unit area (1 m²) of the surrounding wall of a diffuse sound field with acoustic energy density E is:
(where c is the speed of sound)
.................................(3)
This is how it works. Using the acoustic energy density in this diffuse sound field, the theoretical formula for reverberation time can be derived from the equilibrium equation between the energy incident on the entire surrounding wall of the room and the energy absorbed. I will explain the calculation process in the next lesson.
(Excerpt from the email newsletter issued on June 17, 2010)
