Image by Albert Bridge, from commons.wikimedia.org

As autumn approaches, amazing audio appears. Few things are as satisfying as the crunch of a dry leaf underfoot, except the crunch of a leaf under a bicycle, which comes twice: once from the front wheel, and once from the back.

You are walking through Reykjavík, listening to a single e-bike crunch its way down an otherwise empty street. In Iceland, e-bikes ride at exactly $$$10$$$ metres per second, the fastest speed at which the police still pretend not to notice. So the bike covers exactly one centimetre every millisecond. You wonder whether the crunches alone reveal the bike's wheelbase: the distance between the points where its two wheels touch the ground (or, equivalently, between the centres of its wheels).

You hear every crunch, and every leaf is crunched exactly twice: first by the front wheel, and later by the back wheel. You keep an open mind about the bike's dimensions: even a wheelbase of one centimetre or of a hundred kilometres is fine by you.

For example, suppose you hear $$$4$$$ crunches, at milliseconds $$$100$$$, $$$200$$$, $$$300$$$ and $$$400$$$. There are two possible wheelbases.

The first possibility is that the wheelbase is $$$100$$$ centimetres and the two leaves are $$$200$$$ centimetres apart. Then the front wheel crunches the first leaf at $$$100$$$ and the back wheel crunches it at $$$200$$$; the front wheel crunches the second leaf at $$$300$$$ and the back wheel crunches it at $$$400$$$.

The second possibility is that the wheelbase is $$$200$$$ centimetres and the two leaves are $$$100$$$ centimetres apart. Then the front wheel crunches the first leaf at $$$100$$$ and the second leaf at $$$200$$$; the back wheel crunches the first leaf at $$$300$$$ and the second leaf at $$$400$$$.