Which of the following terms suggests a gradual increase in speed?

The term that suggests a gradual increase in speed is "accelerando." This Italian musical term specifically instructs performers to gradually increase the tempo or playing speed of a piece. It creates a sense of forward momentum and excitement in the music.

In contrast, "diminuendo" indicates a gradual decrease in volume, not tempo, which contrasts with the concept of increasing speed. "Crescendo" refers to a gradual increase in loudness, again unrelated to tempo. Lastly, "tempo di Valse" translates to "waltz time," describing a specific rhythmic feel rather than indicating a change in speed. Thus, "accelerando" is the term that directly conveys the idea of accelerating or increasing the pace in music.