Higher-order frequency locking of an organ pipe: A measurement study based on synchronization theory

Higher-order frequency locking of an organ pipe was investigated in terms of relationships between the locking phenomena and the harmonics of the pipe sound and an external force acting onto the pipe. The authors first assumed the pipe as a phase oscillator that is used in synchronization theory and predicted frequency ratios that can cause frequency locking. The authors then forced an actual pipe using a pure tone with frequency ratios of 1: 1, 1: 2, 2: 1, 1: 3, and 2: 3. In addition, experiments were conducted using complex tones to investigate effects of higher harmonics of the external force on frequency locking. As a result, frequency locking occurred only at frequency ratios of 1: 1, 1: 2, and 1: 3 in the case of the pure tone in agreement with the prediction of synchronization theory. For the complex tone, the authors succeeded in inducing 2: 1 locking. The results show that the frequency of a harmonic component of the external force was close to that of the pipe sound when frequency locking occurred. Frequency locking of an organ pipe was therefore enhanced through the proximity of the harmonics of the pipe sound and the external force.