# Comparative Study of Sound Transmission Losses of Sandwich Composite Double Panel Walls
## 2 The Sound Transmission Loss Curve  
To analyze fully the noise transmitted during vibro-acoustic excitation of DPS, the STL curve has to be clearly understood. The curve shows the various frequency regions and also gives the actual characteristics of the material to absorb sound. In the STL characteristics curve, several dip frequencies can be observed which may include the resonance frequency \((f_{R})\), mass-air-mass frequency \((f_{MAM})\), ring frequency \((f_{r})\), critical frequency \((f_{cr})\) and coincidence frequency \((f_{\alpha})\) as expressed by their formulas in Table 1. For unbounded panels with enclosed air cavity, the first dip of the STL curve corresponds to the mass-air-mass frequency \((f_{MAM})\). Resonance frequencies are commonly observed with flat or rectangular DPS while ring and critical frequencies are characteristics of cylindrical or curved DPS [26]. Coincidence frequencies are common to all considered DPS cases. For flat plate or shell, the resonance frequency \((f_{R})\) is the first frequency which occurs when the frequency of the vibrating structure reaches its natural frequency. As stated, this frequency is missing in cylindrical shells, rather a ring frequency \((f_{r})\) which is the first transition frequency is observed as shown in Figure 1b. At this frequency, the longitudinal wavelength equals the circumference of the structural element [27]. The next observed frequency for the cylindrical or curved shell is the critical frequency (\(f_{cr}\)). This is the dip frequency where the circumferential wave number and mode order divided by the radius of shell are equal. The expressions of the critical dip frequency of DPS have been given by [PERSON] et al. [26]. The dip frequency that is common to flat, cylindrical or curved DPS is the coincidence frequency (\(f_{co}\)). At this frequency, the wavelength of the trace velocity of the acoustic wave becomes equal to the bending wave velocity of the DPS. Moreover, the coincident frequency approaches the critical frequency as the incident angle (\(\theta\)) becomes 90 degrees. Table 1 gives the formulas used for calculating these frequencies at different regions. From Table 1, the symbols \(E\), \(R_{s}\), \(\rho\) and \(\
u\) represent Young's modulus, radius of the cylindrical shell, density and Poisson ratio, respectively. While \(h_{s}\) and \(c\) represent the thickness of the cylindrical shells and velocity of flow in the medium, respectively; the symbols \(k\), \(h\), \(A\), \(m_{k}\), \(m_{s1}\), \(m_{s2}\) and \(H\) are stiffness, thickness, area of the piezoelectric patch of resonator, mass of the equivalent spring, surface mass densities of the two panels and distance between the two panels, respectively. Also, these frequencies are key indicators typically used by researchers to analyze the vibro-acoustic response of double panels or shell structures [28; 29; 30]. Several studies of transmission loss for sandwich and composite DPS have revealed various important regions [33]. However, the transmission loss characteristics curve can be generally divided into three regions--the stiffness controlled region, the mass controlled region and the coincidence controlled region [34; 37; 38; 39; 40; 41] as depicted in Figure 1. From the figures, the stiffness controlled region emanating from the origin to the first resonance (\(f_{R}\)) for flat plate or the transition resonance (\(f_{r}\)) for cylindrical or curved shell, is seen as a falling STL curve in the low frequency region. The region of the curve between \(f_{R}\) and \(f_{co}\) for flat or rectangular structure is the mass controlled region. This curve is typically seen as a rising curve and is controlled by the mass law [42]. In some special cases, for flat or rectangular structure, as the stiffness of the material decreases, a damping controlled region could be observed [43; 44]. Moreover, the mass-controlled region is also observed by the cylindrical or curved structures but they are within the \(f_{r}\) and \(f_{cr}\) regime as depicted in Figure 1b.