## 3 Numerical Simulation and Experimental Validation  
Numerical simulations were performed to obtain the normalized FR \(H(\omega)\). During the simulation process, the edges of the SMB were divided into equally sized elements with a size of 1 mm, and a sampling frequency of 100 kHz is adopted. The thickness of the SMB was set to be 10 mm in the simulation. Figure 3 depicts the two normalized FRs simulated with and without the consideration of the diffractions caused by the source on the rear side. This clearly shows that a microspeaker with a flat FR produces an uneven response in the receiver owing to the presence of the SMB. Furthermore, larger fluctuations in the normalized FR curves can be observed when the diffractions caused by the source on the rear side are considered. Relatively large fluctuations exist at frequencies below 1 kHz in both normalized FR curves. Notably, the SMB causes two large peaks at approximately 200 Hz and 600 Hz, as well as a considerable dip at approximately 400 Hz. As the frequency increases, the fluctuation attenuates, which illustrates that higher-frequency waves are more immune to diffraction than lower-frequency waves. Consequently, only diffractions in the low-frequency domain should be considered in practical measurements. Table 1 presents the two normalized FRs in Figure 3 for frequencies between 100 Hz and 1 kHz. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Frequency (Hz)**} & **H(\(\omega\)) Considering the Front-Side Source (dB)** & **H(\(\omega\)) Considering Sources on Both Sides (dB)** \\ \hline
100 & \(-\)0.109 & 0.105 \\
125 & 0.163 & 0.638 \\
160 & 0.509 & 1.142 \\
200 & 0.714 & 1.337 \\
250 & 0.565 & 1.109 \\
315 & \(-\)0.036 & \(-\)0.077 \\
400 & \(-\)0.527 & \(-\)1.114 \\
500 & \(-\)0.129 & \(-\)0.157 \\
630 & 0.286 & 0.541 \\
800 & \(-\)0.081 & \(-\)0.198 \\
1000 & \(-\)0.018 & \(-\)0.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Normalized FRs “H(\(\omega\))” for center frequencies of the 1/3 oct bands between 100 Hz and 1 kHz. Figure 2: Dimensions of the SMB and typical diffraction paths. (**a**) Dimensions of the SMB and (**b**) typical diffraction paths of the SMB. To validate the theoretical analysis and numerical simulations, the normalized FRs \(H(\omega)\) were first measured and thereafter compared to the calculated values. Experiments were performed in the following steps: firstly, the FR of a microspeaker on the SMB was measured in a full anechoic room with size of 11.4 m \(\times\) 7.8 m \(\times\) 6.7 m. Secondly, the FR of the microspeaker was obtained in a hemi-anechoic room with size of 6.5 m \(\times\) 5.5 m\(\times\) 4 m by mounting the microspeaker on the reflecting surface of the hemi-anechoic room. The difference between the two measured sound pressure levels (SPL) is the measured, normalized FR \(H(\omega)\). The experimental setup is shown in Figure 4. A microspeaker driver and a closed-box microspeaker module were chosen as the sources, and a reference microphone (type 4190 L, Bruel & Kjaer) was placed in front of the microspeakers with a measuring distance of 0.1 m. The size of the microspeaker driver is 11 mm \(\times\) 15 mm \(\times\) 3.5 mm and the size of the closed-box microspeaker module is 18 mm \(\times\) 29 mm \(\times\) 12 mm. The SMB used in the experiments is made of aluminum with a thickness of 10 mm. The SPL of the microspeakers was obtained using a PULSE Analyzer (type 3160A, Bruel & Kjaer). Notably, only the front side of the driver will radiate sound in the hemi-anechoic room when a microspeaker driver is measured in the second step. Figure 4: Experimental setup for measuring the normalized FRs. (**a**) Front and side views of the microspeaker driver and, (**b**) front and side views of the closed-box microspeaker module. (**c**) Schematic view of the experimental setup in the anechoic room, and (**d**) in hemi-anechoic room. Figure 3: Normalized FR \(H(\omega)\) with and without the consideration of the diffractions caused by the source on the rear side.