What determines the timbre of a sound?

The timbre of a sound depends on the waveform, which depends on the number of overtones or harmonics that are present, their frequencies and their relative intensity.

In a musical timbre, the characteristic color of the tone of an instrument or voice, resulting from the vocal or instrumental use of different harmonics or overtones of the main tone. The timbre is determined by the shape of the instrument (for example, the tapered or cylindrical pipe of a wind instrument), the range of frequencies within which the instrument can create overtones.