Final answer:
The wave-like motion of a flagellum is produced by the sliding of microtubules propelled by dynein motor proteins within the flagellum's axoneme structure, consisting of a 9+2 microtubule array, allowing eukaryotic flagella to undulate and propel cells, such as sperm.
Step-by-step explanation:
The wave-like motion of a flagellum is produced by the movement of microtubules that slide past one another. This process is driven by dynein motor proteins, which cause adjacent microtubules within the flagellum's structure to move relative to each other. This structure, known as the axoneme, typically consists of a 9+2 array of microtubules (nine parallel pairs surrounding a central pair) in eukaryotic flagella. Eukaryotic flagella, such as those of sperm cells, are more flexible than prokaryotic flagella and undulate in wave-like motions to propel the cell.
In contrast to flagella, cilia are short, hair-like structures that can be found covering the entire surface of certain cells. Cilia's motion is also based on the sliding of microtubules, which allows them to beat back and forth to move substances along the surface of the cell or to move the cell itself, as observed in certain protozoa and respiratory tract cells.