Density waves in a system of non-interacting particles

• Non-interacting balls dropped in a gravitational field can form sharply peaked density waves.
• We explain these waves analytically and discuss their characteristics.
• It may be possible to measure the strength of a gravitational field using these waves.

An ensemble of non-interacting bouncing balls being acted on by a constant gravitational force, starting at rest from a uniform density distribution, will develop a structure of sharply peaked density waves. We describe these waves by computing the density profile of such a system analytically, and we find that the analytical results are in good agreement with numerical findings. We suggest that in a real system, these density waves could be used to produce measurements of the strength of a gravitational field.