Pythagoras first discovered that the vibrations of strings are drastically enhanced at certain frequencies. This discovery forms the basis of our tone system. Such natural vibrations ubiquitously exist in objects regardless of their size scales and are widely utilized to derive their species, constituents, and morphology. For example, molecular vibrations at a terahertz rate have become the most common fingerprints for the identification of chemicals and the structural analysis of large biomolecules.
