Final answer:
To resonate one octave higher than a closed pipe of 20 cm, an open pipe should be 10 cm long to achieve double the frequency at the fundamental resonance. Thus, the answer is (a) 10 cm.
Step-by-step explanation:
The question involves understanding the resonance frequencies of a closed-pipe (also known as a closed-end resonator) and an open-pipe (open at both ends).
For a closed pipe, the fundamental frequency has a node at the closed end and an antinode at the open end. The length of the pipe corresponds to a quarter of the wavelength of the sound wave. In contrast, an open-pipe resonator like a flute has both ends open, which means both ends are antinodes, and the fundamental wavelength is twice the length of the pipe, corresponding to half of the wavelength.
To resonate one octave higher, a sound must have a frequency that is double the original frequency. To achieve this, the length of the open pipe must be half that of the closed pipe for the fundamental frequency. Since your friend's closed pipe is 20 cm, the length of the open pipe resonating one octave higher should be 10 cm. Thus, the answer is (a) 10 cm.