## 4 Result and Discussion
However, for sound power level up to 50 dB, we get broader range of frequency denoted as D, E and F for all taper ratios as reported in Figure 10. It may be inferred from Figures 8-10 that plate with different combinations of point masses plays a significant role in sound power reduction in different frequency bands. For plates with four point masses combinations, the lowest sound power is observed in comparison to one point mass and two point mass combinations. However stiffness contribution due to various taper ratios have very limited impact on sound power level reduction in comparison to that of modes and excitation locations of plate with different combination of point masses. From Figures 8-10, it is observed that for excitation frequencies up to 2000 Hz, the effect of different combinations of point masses and stiffness variation due to different taper ratios do not have a significant effect on sound power radiation for clamped-free forcing boundary condition. However, when the excitation frequency increases beyond 2000 Hz and up to the first peak, Case I plate with one point mass combinationreports the higher sound power level only for a higher taper ratio. However, for Case I plate with two point masses and four point masses combinations, there are variations of the sound power level. This is due to variation of peaks due to different taper ratios at this forcing region. Beyond 2000 Hz, Case II plate with two point massescombinations is seen to have the highest sound power level. However, the sound power for Case III plate is found to be decreased for all combination of point masses. Different modes do influence the sound power peaks as evident from Figures 8-10. Sound power level peak obtained for different modes (0, 0) and (0, 1) is investigated and it is observed that the dissimilar peak for (0, 0) and (0, 1) is observed for plate with different point masses. However, with increasing taper ratio, sound power levels do shift towards lower frequency for all combinations of point masses. It is observed that at higher forcing frequency beyond 4000 Hz, different taper ratios alter its stiffness for different cases of thickness variations. It is needless to mention that for higher frequency beyond 4000 Hz up to 8000 Hz, plate with different combination of point mass alter its stiffness at higher forcing frequency. The acoustic power curve is seen to intersect each other at this high forcing region. Table 7 compares the peak sound power level of different parabolic tapered plate with different combinations of point masses for taper ratio \(\rm T_{x}\) = 0.75. It is interesting to note that the lowest sound power of 76 dB is observed for plate with four point mass combinations among all different thicknesses and the highest power of 82 dB is observed for plate with one point mass combination. Figures 11-13 compares Case I, Case II, and Case III for sound power level numerically for different combinations of point mass for taper ratio, \(\rm T_{x}\) = 0.75. From Figures 11-13 it is investigated that for excitation frequency up to 2000 Hz, plate with different parabolic thickness variations does not have contribute much on sound power radiation. However, beyond excitation frequency of 2000 HZ and up to the first peak, it is investigated that Case II plate with two point masses combination is very good sound radiator of sound power 83 dB in comparison to 82 dB of plate with one point mass combination. Case III plates with all combinations of point masses are seen to have poor sound radiation. Figure 14 compares radiation efficiency (\(\rm\sigma_{mn}\)) analytically and numerically for Case I plate with four point masses combination having parabolically decreasing thickness variation and for taper ratio \(\rm T_{x}\) = 0.75.