A flute is similar to a pipe open at both ends, while a clarinet is similar to a pipe closed at one end. Explain why the fundamental frequency of a flute is about twice that of the clarinet, even though the length of these two instruments is approximately the same

The flute is an open pipe, open at both ends and the clarinet is a closed pipe, closed at one end open at the other. The wavelength of the flute is then twice the length of the pipe while four times that o the clarinet. The flute has antinodes on both ends, while the clarinet only has this on one.