What musical term indicates a speed change without a specified tempo?

The musical term that indicates a speed change without a specified tempo is indeed "Ad libitum." This term derives from Latin, meaning "at one's pleasure." It suggests that a performer has the freedom to interpret the tempo and expressiveness of the music, which allows for spontaneous variations rather than adhering to a strict metronomic pace.

In contrast, "Accelerando" refers specifically to a gradual increase in tempo, providing a clear directive about how the speed should change. "Agitato" denotes a lively or agitated style, usually implying a faster and more intense manner of playing but does not specify a speed change in the same flexible way as "Ad libitum." "Allargando," on the other hand, indicates a gradual slowing down while also broadening the tone but does not convey the same sense of personal interpretation as "Ad libitum."

Thus, the nuance of "Ad libitum" as a term allowing for flexibility and personal judgment makes it the correct choice for indicating a speed change without a specified tempo.