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The authors investigate the impact dynamics of steel balls dropped onto stacks of paper across varying thicknesses under atmospheric and evacuated conditions. Contrary to conventional damping intuition, the coefficient of restitution exhibits a sharp non-monotonic peak where the acoustic round-trip time through the stack synchronizes with impact contact duration. Crucially, this high-restitution "trampoline" effect disappears entirely in a vacuum, proving that trapped interstitial air—rather than solid elastic response—drives the acoustic recovery.
Trapped interstitial air transforms ordinary paper stacks into resonant acoustic trampolines, triggering a massive rebound peak whenever acoustic wave transit times match impact duration.
A ball bouncing on a thicker cushion should bounce less. We show that this is not always so . Measuring the coefficient of restitution $e$ of a steel ball dropped on a stack of $N$ sheets of standard A4 printer paper, we find that $e$ first drops, then rises to a pronounced maximum, and only then decreases towards a minimum. The maximum occurs where the acoustic round trip through the stack matches the contact time of the impact. For a contact set by the stack itself, one recovers the classical bar-impact condition of a stack-to-ball mass ratio of order one. Bar impact, however, predicts only a weak recovery, insensitive to the surrounding gas. For paper stacks, the recovery is large and no maximum is resolved when the stack is evacuated: the air trapped between the sheets, not the paper alone, makes the stack a trampoline.