Final answer:
The lowest note on a clarinet is about half the frequency of that on a flute because the clarinet is a tube closed at one end and behaves as an open-closed tube, producing a lower fundamental frequency than the flute, which acts as an open-open tube.
Step-by-step explanation:
The reason the clarinet can produce a note about half the frequency of that on a flute, despite being of similar length, is due to the way the air column behaves when the instrument is played. While both instruments use the principle of changing the length of the resonating air column to produce different frequencies, the flute is effectively open at both ends while the clarinet is open at one end and closed at the other because of the mouthpiece and reed. This means that the flute acts as an open-open tube and the clarinet as an open-closed tube. For open-closed tubes, the lowest frequency produced (the fundamental frequency) is lower compared to an open-open tube of the same length.
The correct answer to the student's question is then not related to bore diameter, reed length, the number of keys, nor the use of a double reed. Instead, it is the behaviour of the resonating air column in an instrument that is closed at one end, like the clarinet, that results in a lower pitch for its lowest note compared to an instrument open at both ends, like the flute.