Question

the waveform of a flute is much simpler than that of an clarinet，why？

Answer 1

Clarinet and flute are two important members of the woodwind family of instruments. The main difference between clarinet and flute is the presence/absence of reeds; flutes are reedless instruments whereas clarinets have a single reed. In addition, the clarinet is an end-blown instrument whereas flute (western concert) is a side-blown instrument.

There is a very fundamental physics (and, consequently, tonal) difference between the two:

• A flute behaves as a pipe resonator that is open on both ends.
• A clarinet, in contrast, is a resonator that is effectively closed at mouthpiece side.

For this reason, in addition to the base tone at frequency f, a flute will produce sound at 2f, 3f, 4f, 5f, … while a clarinet on the other hand will sound only at f and its odd higher harmonics: 3f, 5f, 7f, …
This gives the two instruments distinctly different characters and affects overtone use in playing.

The clarinet makes a soft, warm, mellow sound and the flute makes a shrill, almost desperate sound.