The Dependence of Flue Pipe Airflow Parameters on the Proximity of an Obstacle to the Pipe's Mouth

Abstract

This paper describes the influence of the presence of an obstacle near the flue pipe's mouth on the air jet, which directly affects the parameters of the sound generated by the flue pipe. Labial pipes of the most common types of mouth were tested. The method of interval calculus was used instead of invasive measuring instruments. The obtained results prove that the proximity of an obstacle affects the sound's fundamental frequency, as the airflow speed coming out of the flue pipe's mouth changes. The relationship between the airflow speed, the value of the Reynolds number, and the Strouhal number was also established. The thesis of the influence of the proximity of an obstacle on the fundamental frequency of the sound of a flue pipe was generalized, and formulas for calculating the untuning of the sound of the pipe were presented for various types of mouth.

Keywords: flue pipe; obstacle; organ tuning; pipe’s mouth.

Figure 1

The position of the microphones during recording: (a) front view, (b) side view.

Figure 2

The interval of the fundamental frequency changes in relation to the distance between the obstacle and the pipe lip of Flute 4-foot D sharp.

Figure 3

The spectrum of the Bass Principal 16-foot D pipe at the lip (red dotted plot) and the top (grey solid line plot) after normalization to the maximum sound level value for the immediate proximity of the obstacle (0 mm) at the pipe’s lip. As we can see, the harmonics do not overlap. The fundamental frequency, calculated by DTFT with 0.01 Hz frequency resolution, is 69.91 Hz at the lip and 69.69 Hz at the top (a difference of about 5 cents, which can be heard by a trained musician, especially when such a sound is accompanied by another playing pipe).

Figure 4

Dolce Flute 4-foot B spectrum for the immediate proximity to the obstacle (0 mm) at the pipe lip. A linear frequency scale has been used to help locate harmonics that are equally spaced on this scale.

Figure 5

The structure of a flue (labial) pipe.

Figure 6

The dependence of the distance of the obstacle from the lips for the Bass Principal 16ft open D.

Figure 7

The comparison of the plots representing the dependence of the fundamental frequency f₀ on the distance of the obstacle x from the pipe’s mouth for Flute 4ft open D sharp. The grey squares represent the measured data (using DTFT). The grey solid line plot shows the interpolated fundamental frequency for the measured data. The red dotted plot shows data calculated from Equation (25).