In the previous installment, we discussed sound transmission and absorption measured based on reverberation time. This time, we will theoretically trace the meaning of the formula for calculating sound transmission loss measured using a reverberation chamber.
The acoustic transmission loss R is given by the following formula, which is 10 times the common logarithm of the ratio of the acoustic power W1 incident on the sample to the acoustic power W2 transmitted through the sample:
(dB)
As mentioned previously, the sound transmission loss in a test facility combining [reverberation chamber - reverberation chamber] is measured using the following process.
Random noise is output from the sound source room, and the average sound pressure level of the sound that has sufficiently diffused within the sound source room and the average sound pressure level of the sound that has passed through the sample and radiated and diffused into the receiving room are measured. Furthermore, the acoustic transmission loss is calculated from the reverberation time of the receiving room using the following formula.
(dB)
Here;
L1: Mean indoor sound pressure level (dB) in the sound source room.
L2: Average sound pressure level (dB) in the receiving room.
F: Area of the sample (m²) equal to the area of the open sample.
A: Equivalent sound absorption area of the sound receiving room (m²)
Furthermore, the equivalent sound absorption area A is calculated using the following formula.
（m2）
Here;
V: Volume of the sound receiving room (m³)
T: Reverberation time of the receiving room (s)
To derive this equation, let's consider the exchange of sound energy between two reverberation chambers.
Let E be the energy density. The acoustic energy incident per second on a unit area (1 m²) of the surrounding wall of a diffuse sound field can be expressed by the following equation (1), as shown in "Chapter 15: Reverberation Theory and Measurement of Reverberation Time Part 1: Diffuse Sound Field".
Here;
E: Energy density of the diffuse sound field
c: speed of sound
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Figure 1
As shown in Figure 1 above, let the energy densities of the sound source chamber and the sound receiving chamber be E1 and E2, respectively. First, considering the energy Es of the sound incident on a sample of area F from the sound source chamber, from equation (1):
Therefore, the energy E sp entering the adjacent room is, if the transmittance is τ, then:
;
On the other hand, on the receiving room side, if the indoor surface area is S, the energy Er incident on the entire wall surface is given by equation (1):
If the average sound absorption coefficient is α, then the energy Era absorbed by the entire wall surface is:
Thus, in a steady state, assuming that the incoming energy is in equilibrium with the sound energy absorbed on the receiving chamber side, we have Esp = Era. That is;
If the average sound pressure levels of the sound source room and the sound receiving room are L1 and L2, respectively, then the difference in sound pressure levels between the rooms is:
If the volume of the sound-receiving room is V and the reverberation time is T, then;
(At a temperature of 20°C, K=0.16)
By measuring the reverberation time of the receiving room and determining Sα from equation (11), and substituting this into equation (10), R can be determined from the average sound pressure levels of the sound source room and the receiving room.
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Ono Sokki "Measurement of Acoustic Transmission Loss Using the Reverberation Chamber Method"
(Excerpt from the email newsletter issued on February 17, 2011)
