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Head flapping has often been considered to be deleterious for obtaining a tonpilz transducer with broadband, high power performance. In the present work, broadband, high power tonpilz transducers have been designed using the finite element (FE) method. Optimized vibrational modes including the flapping mode of the head are effectively used to achieve the broadband performance. The behavior of the transducer in its longitudinal piston mode and in its flapping mode is analysed for in-air and in-water situations. For the 37.8% bandwidth of the center frequency from 28.5 to 41.8 kHz, the amplitude variation of the transmitting voltage response (TVR) does not exceed /spl plusmn/2 dB and a maximum TVR of 146.8 dB (ref. 1 /spl mu/Pa/volt at 1 meter) is obtained. Reasonable agreement between the experimental results and the numerical results is achieved. A maximum sound pressure level of 214.8 dB can be expected. Further numerical calculation indicates that there is potential for increasing the bandwidth by varying other parameters in the design.