## 4 Result and Discussion
It is observed that on comparison the results obtained for radiation efficiency matches well with each other as reported in Figure 14. Figure 15 compares the variation of radiation efficiency for Case I plate (parabolic decreasing thickness variation) with different arrangement of point masses for different taper parameter \(\rm T_{x}\). In this numerical simulation, it is found that for exciting frequencies up to 1000 HZ, the effect of radiation efficiency with different arrangement of point masses and for different taper ratios is independent of excitation frequency. However, at a given forcing frequency beyond 1000 HZ, higher taper ratios cause higher radiation efficiency as evident from Figure 15. It can also be seen that with increasing taper ratio sound power level peaks do shift towards lower frequency as reported in Figure 15. Moreover, beyond 2000 HZ, different taper ratios alter its stiffness at higher frequency and radiation efficiency curve tends to intersect each other at this high forcing region. It can also be seen that all radiation curves due to all combination of point masses tends converge in a frequency range of 6800-7200 HZ and clear peaks are seen at this frequency band. From Figure 15, it is noted that with increasing taper ratio the radiation efficiency increases for all combination of point masses. Among these radiation combinations, the highest radiation efficiency is shown by Case II plate with two point mass combinztions. The moderate radiation efficiency is seen to be observed for Case I plate with one point mass and two point masses combinations as reported in Table 7. However, at higher forcing frequencies, different parabolic tapered plate (Cases I, II, and III) with four point masses combination shows the least radiation efficiency as evident from Figure 7.0 It is interesting to note that the lowest radiation efficiency (\(\rm\sigma_{mn}\)) is shown by Case III plate. Thus, Case III plate may be considered a poor radiator among all the thickness variation with different combinations of and point masses. Figure 16 compares the radiation efficiency numerically for plates with different parabolic thickness variation two point masses combination for taper ratio \(\rm T_{x}\) = 0.75. It is investigated that all cases of parabolic tapered plate contribute almost the same radiation efficiency as depicted from Figure 7.1 Figure 17 shows the numerical comparison of sound power level for plate with two point masses combination for different parabolic thickness variation and for taper ratio \(\rm T_{x}\) = 0.75. It is observed that almost equal and increasing peak sound power level is seen for all cases of parabolic tapered plate. Hence, the stiffness variation due to different taper ratios has negligible effect on acoustic radiation as evident from Figures 16 and 17. Figure 7.2 Numerical comparison of sound power level for Case I plate with one point mass having parabolic decreasing thickness variation with different taper ratio \(\rm T_{x}\). Figure 7.3 Analytical and numerical comparison of sound power level for Case I plate with four point masses having parabolic decreasing thickness variation for taper ratio \(\rm T_{x}\) = 0.75. Figure 7.4 Numerical comparison of sound power level for Case I plate with two point masses having parabolic decreasing thickness variation with different taper ratio \(\rm T_{x}\). Figure 7.5 Numerical comparison of sound power level for Case I plate having parabolic decreasing thickness variation for different combinations of point masses for taper ratio T\({}_{\rm x}\) = 0.75. Figure 7.6 Numerical comparison of sound power level for Case II plate having parabolic decreasing increasing thickness variation for different combinations of point masses for taper ratio T\({}_{\rm x}\) = 0.75. Figure 7.7 Numerical comparison of sound power level for Case I plate with four point masses having parabolic decreasing thickness variation with different taper ratio T\({}_{\rm x}\).