Sound analysis of a cup drum

The International Young Physicists? Tournament (IYPT) is a worldwide tournament that evaluates a high-school student's ability to solve various physics conundrums that have not been fully resolved in the past. The research presented here is my solution to the cup drum problem. The physics behind a cup drum has never been explored or modelled. A cup drum is a musical instrument that can generate different frequencies and amplitudes depending on the location of a cup held upside-down over, on or under a water surface. The tapping sound of a cup drum can be divided into two components: standing waves and plate vibration. By individually researching the nature of these two sounds, I arrived at conclusions that could accurately predict the frequencies in most cases. When the drum is very close to the surface, qualitative explanations are given. In addition, I examined the trend of the tapping sound amplitude at various distances and qualitatively explained the experimental results.