Final answer:
The fast Bohemian dance with alternating slow and fast sections is called the Polka. It integrates a melancholic melody with a joyful rhythm in a 2/4 time signature.
Step-by-step explanation:
The name of the fast Bohemian dance that alternates between a slow, sad section and a fast, happy one is the Polka. This dance has its roots in Bohemia, part of the modern-day Czech Republic. It became popular across Europe in the 19th century and spread to other parts of the world. The key hallmark of the Polka is its rhythmic pattern which is characteristically performed in a quick 2/4 time.
The slow section of Polka often conveys a more melodic, sorrowful feel, which then transitions into a lively, buoyant section as the tempo increases.