Why do a metal flute and a wooden flute produce similar sounds?

A metal flute and a wooden flute produce similar sounds because they are both classified as aerophones, specifically edge-blown instruments, where the primary vibrating medium is the air column contained within the tube rather than the material of the instrument itself.12

In these instruments, sound is generated through a process called edge-tone generation. The player directs a stream of air against a sharp edge, which causes the air to split and creates vibrations within the enclosed air column. Because the air column is the source of the vibration, the acoustic principles remain consistent regardless of whether the tube is constructed from metal, wood, or other materials.12

While the material of an instrument can influence its tonal qualities, the classification of flutes as "woodwinds" is based on their method of sound production rather than their composition. Consequently, modern flutes—often made of metal like silver or gold—and traditional wooden flutes both rely on the same fundamental physics to produce their characteristic clear, sustained pitch.21