Ultrasound, whether sensing or actuating, is employed in a wide variety of applications including medical imaging, nondestructive evaluation, industrial cleaning, therapeutic ultrasound and dental ultrasonics [1,2]. Electrostatic ultrasonic transducers are used for the detection and generation of ultrasonic waves . These transducers consist of a thin dielectric membrane stretched across a conducting backplate, which is often rough or grooved in order to trap air beneath the membrane and reduce the membrane’s rigidity . Many factors in the transducers design will affect the performance of the transducer; such factors include the membrane thickness and size [5,6], the dimensions and design of the backplate , and the voltages applied . One difficulty in the application of these transducers lies in the impedance matching into air, or any other fluid. Traditional piezoelectric transducers require the use of air backing and a porous matching layer in order to achieve acceptable sensitivity [3,8,9]. While capacitive micromachined ultrasonic transducers (cMUTs) are better matched to air, there is still an impedance difference of up to an order of magnitude. One approach to reduce this impedance gap, and so enhance the device efficiency, is that of incorporating resonating cavities (as are often found in musical instruments) in the conducting backplate. Acknowledging this, Campbell et al.  considered the inclusion of resonating conduits connected to the cavities in the backplate. The experimental results suggested that the inclusion of fluid filled conduits in the backplate design can increase the amplitude of operation of the electrostatic transducer.
This research [11,12,13] considers theoretical models of this electrostatic transducer and transducers which employ ideas to increase the amplitude of operation. The designs consists of a metallised Mylar membrane stretched over a brass backplate with design features such as air filled cavities and adjoining conduits or Helmhotlz resonators. The important outputs from the models are the electrical and mechanical impedances of the device, the pressure transmitted by the membrane into a fluid load, and the transmission and reception sensitivities. Models considered are one-dimensional (in space), membrane models and plate models.
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 A. J. Walker and A. J. Mulholland, A theoretical model of an electrostatic ultrasonic transducer incorporating resonating conduits, IMA J. Appl. Math., 2010.
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 A. J. Walker and A. J. Mulholland, A Theoretical Model of an Ultrasonic Transducer Incorporating Spherical Resonators, IMA Journal of Applied Mathematics (submitted)