# Advanced Rating Method of Airborne Sound Insulation
## 3 Measured and Calculated Values
### Sound Level of Interest  
After transmission of the source signal (\(L_{1}\)) through a structure or partition (\(R_{w}\), \(D_{nT}\)), the sound heard by a listener is the receiving sound signal (\(L_{2}\)). The filtered level (\(L_{2}\)) contains all the information of the airborne sound insulation characterized by the weighted apparent sound reduction index (\(R\)'\({}_{w}\)) as it is the transmitted sound signal. The sound level of interest (\(L_{2}\)) is, in this study, the electronically filtered sound sample, which is obtained using a filter function representing the sound insulation (\(R_{w}\)) of interest. The filter function, i.e., the transfer function used in the software, is generated by modeling the \(R\)-values as the coefficients of a built transfer function. The phon is a unit of perceived loudness level (\(L_{N}\)), which is a subjective measure of the strength of a sound so that the measure of sound insulation is written in terms of a loudness level. Thus, the heard sound, which is the sound level of interest (\(L_{2}\)), is assessed in terms of a loudness level \(L_{N}\).  
If the loudness level (\(L_{N}\)) of the sound signals used in this study is calculated for different sound pressure levels, it is observed that there is no linear correlation between both measures. This is illustrated in Figure 2, where the loudness level is depicted over sound pressure level.  
From Figure 2, it is seen that the loudness level is not linearly related to the sound pressure level and is dependent on the type of signal. Even for an equal sound pressure level, the calculated loudness level differs in its absolute value depending on the type of signal. Inspection of this data shows that varying the sound signal, i.e., using a broadband noise signal and a transient signal, leads to somewhat different results, allowing the sound pressure level to remain constant. This means that the loudness of a broadband sound and that of a transient signal are different. This is in agreement with the literature [12].  
Figure 1: Time signal of white noise (WN), pink noise (PN), Eminem (E), Beethoven (B), and Party Sound (PS) with equivalent continuous sound pressure level of 85 dB and duration of 90 s.  
The calculated psychoacoustic parameter specific fluctuation strength (_Fls'_) is also not a linear function and is also dependent on the type of signal and on the level of the sound signal. In Figure 3, the region of the specific fluctuation strength (_Fls'_) of the sound signals used in this study is depicted as a function of sound pressure level.  
It is seen that the broadband noise signal has little specific fluctuation strength, whereas the transient signal, i.e., music-type signal, spreads with increasing sound pressure level. This means  
Figure 3: Specific fluctuation strength (_Fls’_) as a function of sound pressure level. The shaded area characterizes the region for the specific fluctuation strength (_Fls’_).  
Figure 2: Loudness level (\(L_{N}\)) as a function of sound pressure level for different sound signals including transient and steady state signals. The shaded area characterizes the region for the loudness level (\(L_{N}\)). The straight line corresponds to the following relationship: sound pressure level = loudness level.  
that the specific fluctuation strength depends on the level of the signal. For very low sound pressure levels, i.e., below approximately 10 dB, both signal types tend to be close to zero. The smallest values are observed using white noise, and the maximum values are identified for the music-type signal E. The deviation of the studied signal types, i.e., the difference between a broadband noise signal and a music-type signal, was observed to be as large as a factor of approximately 100.