Input impedance of asian free-reed mouth organs

The khaen, naw, bawu, and sheng are examples of Asian free-reed mouth organs, which incorporate free reeds coupled to pipe resonators. Previous research has shown that the reeds in these instruments behave as blown-open reeds: the playing frequency is above both the natural frequency of the reed and the first peak of the measured impedance curve. Detailed calculations of input impedance have been made for a variety of these instruments, taking into account the position of the reed along the pipe, tuning slots, finger holes, and noncircular cross sections. The details of these calculations are in good agreement with the measured impedances of the same instruments, even in the higher harmonics. A study of the coupling of the free reed and pipe resonator has provided additional details about the influence of the pipe impedance on the playing frequency and sound spectrum of the reed-pipe combination. [Research supported by NSF REU Grant PHY-0354058.]