# Improved Sound Radiation of Flat Panel Loudspeakers Using the Local Air Spring Effect
## 3 Numerical Analysis of the Pressure Deviations
### Evaluation of both Decomposition Methods  
Figure 7 shows both decomposition methods. The modal-related decomposition shows the amount of every single driven mode. All even-numbered modes are not excited and have no effect on the overall performance. Therefore, these modes are not presented. It becomes clear that the excitation of every mode will result in a peak in the frequency response. Therefore, it is crucial to increase the modal density and find a position of the exciter that excites almost all modes. The frequency response between the two modes is critical and can result in an acoustic addition or subtraction dependent on the individual radiation area and phase. It can be concluded that the conversion from one mode to another mode can result in a new shape, resulting in strong acoustic cancellation or in acoustic addition with higher output. \(SPL_{Mode1}\) represents a reasonable reference to estimate higher output through individual modes or the acoustic cancellation caused by individual modes. To analyze this in more detail, Figure 7 is subdivided into five areas (I-V).  
* **Area I (20-80 Hz):** In the lower frequency range, only \(SPL_{Mode1}\) and \(SPL_{Mode3}\) contribute to overall performance. The pressure response of \(SPL_{Total}\) is lower than the response of \(SPL_{Model1}\). This shows an anti-phase component of \(SPL_{Mode3}\), which minimizes the \(SPL_{Total}\). Furthermore, the \(SPL_{Total}\) is close to the \(AAL_{Total}\), and the radiation is nearly ideal. There are only a small number of anti-phase components in addition to the in-phase components.
* **Area II (80-102 Hz):** This area shows a positive modal overlay. The pressure of \(SPL_{Total}\) is higher than the response of \(SPL_{Mode1}\) or \(SPL_{Mode3}\). After the resonance of \(SPL_{Mode1}\), a phase shift occurs, and \(SPL_{Mode1}\) and \(SPL_{Mode3}\) radiate in phase. This is also visible by the reduced level of the anti-phase components.
* **Area III (102 Hz-165 Hz):** This band shows a significant dip at 110 Hz. \(SPL_{Mode1}\) and \(SPL_{Mode3}\) contribute nearly at a similar level, whereby \(SPL_{Mode3}\) has a higher contribution than \(SPL_{Mode1}\), especially at 110 Hz. The resulting level of the \(SPL_{Total}\) is lower compared to \(SPL_{Mode1}\) and \(SPL_{Mode3}\), and the amounts of in-phase and anti-phase components are nearly equal. Therefore, the resulting radiating area is reduced. The result is substantial surface movement with less radiation.
* **Area IV (165-265 Hz):** This band shows the possibility of an in-phase overlay of modes. The \(SPL_{Total}\) is higher than the response of \(SPL_{Mode1}\), \(SPL_{Mode3}\) or \(SPL_{Mode8}\). \(SPL_{Mode1}\) and \(SPL_{Mode8}\) are radiating in phase. The level differences of the in-phase and anti-phase components are 5-10 dB, which results in a larger radiating surface area and a high output.
* **Area V (265-1000 Hz):** This band shows in-phase and anti-phase overlays of the modes. The \(SPL_{Total}\) is at certain frequencies higher and lower than the radiation of \(SPL_{Mode1}\). This visualizes the modes that are not radiating in phase with \(SPL_{Mode1}\) and will reduce the overall output. Furthermore, the level difference of the in-phase and anti-phase components are reduced, which will end up in a smaller radiating surface area, even if substantial motion occurs on the surface. The \(AAL_{Total}\) does not decrease to higher frequencies.