Source strength relations for the Boehm flute Free

The flute is unusual among woodwinds because it radiates sound from the embouchure hole and from its tone holes. Coltman (1969) showed accurately equal source strengths at the blown and unblown mouths of a double‐ended organ pipe. On a flute the standing wave flow divides: Part enters the compliance of the headjoint cavity, and part traverses the embouchure hole into the room. Similarly, some flow exists from the first tone hole, and the (attenuated) remainder travels toward the other holes. Calculation shows the source strength ratio S_emb/S_{first hole} is roughly constant (+3 dB) below 1 kHz, 0 dB 1.55 kHz and −3 dB at 1.8 kHz. The summed effect of all the tone holes subtracts 6 dB from the figures given. Above the tone hole cutoff frequency (≃2 kHz) the ratio can be anywhere between −2 dB and +5 dB. Experiment confirms all this for a first class silver flute playing mezzoforte G₄. The overall S/N ratio is 46 dB at the embouchure hole, and considerably better at the tone hole. The frequency dependence of the noise source ratio is unlike that of the signal: the noise is thus not associated with the standing wave. The free space radiated angular distribution is little affected by S_emb/S_hole ≠ 1. Even partials show a notch near the equatorial plane; odd partials radiate preferentially in a similar direction. In a room the two sources add incoherently since their spacing exceeds the room's autocorrelation distance. [Work supported by NSF.]