Detecting the mass and position of an adsorbate on a drum resonator

The resonant frequency shifts of a circular membrane caused by an adsorbate are the sensing mechanism for a drum resonator. The adsorbate mass and position are the two major (unknown) parameters determining the resonant frequency shifts. There are infinite combinations of mass and position which can cause the same shift of one resonant frequency. Finding the mass and position of an adsorbate from the experimentally measured resonant frequencies forms an inverse problem. This study presents a straightforward method to determine the adsorbate mass and position by using the changes of two resonant frequencies. Because detecting the position of an adsorbate can be extremely difficult, especially when the adsorbate is as small as an atom or a molecule, this new inverse problem-solving method should be of some help to the mass resonator sensor application of detecting a single adsorbate. How to apply this method to the case of multiple adsorbates is also discussed.