Final answer:
The smallest member of the flute family that sounds an octave higher than an ordinary flute is the Piccolo. Instruments like the piccolo produce higher-pitched sounds due to their shorter air columns. The Piccolo, Recorder, Ocarina, and Clarinet are all wind instruments, but the Piccolo is the one that matches the given description.
Step-by-step explanation:
The smallest member of the flute family that sounds an octave higher than an ordinary flute is the Piccolo. This is because smaller instruments like the piccolo have a shorter air column compared to larger instruments such as tubas, which results in higher frequencies of sound, or higher pitches. The recorder, ocarina, and clarinet are also wind instruments, but they do not match the description provided.
When discussing the physics of how instruments create sound, it is important to consider that instruments such as flutes and oboes, which are open-pipe resonators, allow players to alter the pitch by varying the length of the tube through opening and closing finger holes. In contrast, instruments like bugles, which have a fixed length, can produce only a limited range of frequencies.
Thus, the correct answer to which is the smallest member of the flute family that sounds an octave higher than an ordinary flute is A) Piccolo.