Thomas Young, a British scientist, was one of the first to explore this question. He invented the double-slit experiment to determine whether light behaves as a wave or as a collection of particles.

The basic idea is to study a beam of objects whose nature is unknown and observe how they behave. There are typical wave behaviors that particles do not exhibit. Observing one of these behaviors demonstrates that the objects in the used beam are waves.

Young decided to take advantage of one of the characteristics of waves: the phenomenon called diffraction, which occurs when waves encounter small obstacles or pass through small openings.

To know all the details, read the articles on diffraction and on Young's experiment, known as the double-slit experiment.