Quantum mechanics is a notoriously difficult subject to learn, due to a lack of real-world analogies that might help provide an intuitive grasp of the underlying ideas. Discrete energy levels and absorption and emission wavelengths in atoms are sometimes described as uniquely quantum phenomena, but are actually general to spatially confined waves of any sort. Here, we provide an experiment demonstrating the acoustic spectroscopy of a drum. We show that a struck drum emits sounds of discrete frequencies (tones), and that the lifetime of each emitted tone is directly related by Heisenberg's uncertainty principle to its line width in the drum's frequency spectrum. We also show that a still drum absorbs only those same frequencies when exposed to monochromatic sound from an audio speaker. The resonant motion of the drum membrane is too fast to see by eye (>60 Hz), but can be observed with the aid of a strobe light. The observed resonant modes of the drum are the eigenfunctions of a particle trapped in an infinite circular well, and analogous to the shapes of atomic orbitals (1s, 2p, 3d, 2s, etc.). This experiment can be built for under $50, and is an excellent demo or lab exercise for general and physical chemistry courses to provide a visual example of abstract quantum mechanical ideas.