In the previous article, we outlined the most common method for measuring the sound absorption performance of materials: the random incident sound absorption coefficient. This time, we will explain the derivation of the formula shown last time.
The reverberation time of a reverberation chamber when no sample is present can be expressed by the following equation, derived from Sabine's reverberation equation (Equation (2) in "Fundamentals of Sound Measurement - Part 16 "Reverberation Theory and Measurement of Reverberation Time" Part 2 - Derivation of Sabine's Reverberation Time Theory Equation").
.................................（1）
T1: Reverberation time (seconds) of a room without a sample
K = 55.3 / c [c: Speed of sound (m/s)]
V: Chamber volume (m 3)
A1: Equivalent sound absorption area of a room without a sample (m²) 2)
A1=S1a1.................................（2）
S1: Total surface area of the room (m²)
α1: Sound absorption coefficient of the room surface
Furthermore, the reverberation time of the room when the sample is placed inside is:
.................................（3）
T2: Reverberation time of the room when the sample is placed inside (seconds)
A2: Equivalent sound absorption area of the room when the sample is placed inside (m²)
A2=S2a2+（S1-S2）a2.................................（4）
S1: Total surface area of the room (m²)
S2: Sample area (m²)
α1: Sound absorption coefficient of room surfaces other than the sample surface
α2: Sound absorption coefficient of the sample
Assuming that the sample area is negligibly small compared to the total surface area of the chamber, equation (4) becomes:
A2=S2a2+S1a1................................（5）
Therefore, from equation (2):
A2=S2a2+A1.................................（6）
From equation (6):
.................................（7）
Therefore, from A2 and A1 in equations (1) and (3):
.................................（8）
We can provide it.
If we move S2 to the left side, we can see that equation (8) corresponds to equation (1) shown previously.
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(Excerpt from the email newsletter issued on May 26, 2011)
