Fischietto e ocarina en

From "Physics, Waves, Music": a website about the physics of waves and sound, acoustics of musical instruments, musical scales, harmony and music.

AI-translated from Italian. Original page: Fischietto_e_ocarina

Structure of the instrument

These are rather compact instruments, in which a narrow, short mouthpiece leads to a roundish resonance chamber. Unlike almost all other wind instruments, the resonance chamber is not cylindrical, and therefore its natural frequencies are given by its Helmholtz resonance. While in the whistle this frequency is fixed, in the ocarina different frequencies can be produced by opening or closing various holes made in the body of the instrument. Since the cavity is much smaller than the wavelength, only the total area of the open holes matters, not their position: opening more holes raises the frequency (in the flute, instead, what matters is the position of the first open hole along the bore).

How the sound is produced

As in all wind instruments, the sound is produced by turning a steady air flow generated by the player's breath into an oscillating flow, and by amplifying the pressure wave thus produced through the resonance of the body of the instrument.

Let us look at this mechanism in more detail.

The source of the oscillations

  • The steady air flow produced by the player, channelled into the mouthpiece, breaks against a sharp edge.
  • Part of the flow enters the resonance chamber and increases its pressure.
  • When the pressure in the chamber equals the pressure of the air flow, the chamber cannot take in any more air, and the flow is directed towards the outside of the instrument.
  • The air in the chamber, compressed like a spring, can now decompress, producing a pressure wave.
  • When the pressure in the chamber has dropped sufficiently again, the air flow can once more enter it from the mouthpiece, producing a second compression and starting the cycle again. The overall frequency of the cycle depends essentially on the size of the cavity, being determined by its Helmholtz resonance.

The very hole that splits the air flow acts as the main radiator of the sound, coupling the oscillations of the air inside the resonance chamber with the surrounding air.

How the timbre is formed

  • It should be noted that the overall dimensions of the cavity are in general much smaller than the wavelength of the sound produced. Therefore the resonances of the higher harmonics that are normally heard in larger spaces such as a room (see standing waves in 3D, architectural acoustics) occur at extremely high frequencies.
  • For this reason the production of higher harmonics is strongly inhibited by the inertance of the radiating hole. Indeed, at high frequencies the acoustic impedance of the instrument is determined essentially by the inertance of the hole (that is, ultimately, by its size).
  • Consequently, the sound emitted by these instruments is essentially a pure tone at the fundamental frequency of the cavity.

Characteristic notes

Acoustic characteristics

As already observed, given the small size of the resonant cavity compared with the emitted wavelengths, in these instruments there is a strong attenuation of the harmonics above the fundamental. As a result the sound is very close to a pure tone, as shown by the waveforms reported below.

Bottles as resonators

f (Hz) V/V0 ff0 V0V
119 1 1 1
151 23 1.27 1.22
209 13 1.76 1.73
We "played" a 1.5 l plastic bottle of rather irregular shape. The body is roughly a parallelepiped with several grooves. A truncated pyramid connects it to the mouth. Playing the empty bottle, and then filling it to one third and to two thirds of its volume, we obtain approximate frequencies of 119, 151 and 209 Hz. The ratios to the lowest frequency are therefore 1, 1.27, 1.76. These ratios are in good agreement with the ratios of the inverse square root of the volume, 1, 1.22, 1.73, predicted by the law of Helmholtz resonators. Note, however, that for a more rigorous experiment one should use a stiffer bottle, which does not take part in the vibration with its high compliance. In all the examples, besides the fundamental, several much weaker higher harmonics are also clearly visible: they are not resonances of the cavity, but come from the air jet, which does not oscillate in an exactly sinusoidal way. The broadband noise, instead, is associated with the turbulent part of the motion of the air flow breaking on the edge of the mouth.


waveform sonogram Audio

BOT_Grande.mp3

BOT_Grande

waveform sonogram Audio

BOT_GrandeUnTerzo.mp3

BOT_GrandeUnTerzo

waveform sonogram Audio

BOT_GrandeDueTerzi.mp3

BOT_GrandeDueTerzi


Harmonic sounds

To make these samples we used a half-litre plastic bottle. Its fundamental frequency corresponds to about 199 Hz. Obviously this value cannot be compared directly with that of the larger bottle, since all the dimensions are different, not only the enclosed volume of air. Note that the fundamental of the bottle corresponds to about 200 Hz. The fundamental tone is accompanied by only four visible higher harmonics, and by a sequence of high-frequency noise bands.

waveform sonogram Audio

BOT_Piccola.mp3

BOT_Piccola

Harmonic sounds can be obtained even from such a rudimentary instrument. In the sound example reproduced here we blew hard into the half-litre bottle. Listening and analysing the sonogram reveal that the loudest sound, audible in the central section of the sample, corresponds to a frequency of 1150 Hz. Towards the end of the sample, in the short time in which the air flow returns to low speeds, the fundamental at 199 Hz emerges again. The sound at 1150 Hz is not a harmonic of the fundamental (1150/199 ≈ 5.8 is not a whole number): it is a higher resonance of the bottle, that is, a standing wave inside the cavity, which the fast air jet manages to excite. Listening very carefully, and looking at the sonogram, one can also isolate a second, higher harmonic right at the beginning, at the centre of a band around 2970 Hz. It gives a hissing colour to the whistle. Other broad, inharmonic bands are part of the noise of the whistle, while a sequence of weak lines in harmonic ratios with the 1150 Hz line is visible, although barely audible in the unfiltered sample.

waveform sonogram Audio

BOT_PiccolaArmonico.mp3

BOT_PiccolaArmonico

Check your understanding

An empty bottle sounds at 119 Hz. At what frequency does it sound if it is half filled with water? Answer. The Helmholtz frequency is inversely proportional to the square root of the air volume: halving the volume raises the frequency by a factor √2, to about 168 Hz.

Why is the sound of an ocarina almost a pure tone? Answer. Because the cavity is much smaller than the wavelength: apart from the Helmholtz resonance it has no other resonances up to very high frequencies, and there are none at two, three, four times the fundamental to reinforce the harmonics.

In an ocarina, does it matter which hole is opened, or only how many? Answer. What matters is the total area of the open holes, not their position: the cavity behaves as a Helmholtz resonator and its frequency increases with the area of the openings. In the flute, instead, what matters is the position of the first open hole, which sets the effective length of the bore.

Blowing hard into the half-litre bottle (fundamental 199 Hz) you hear a whistle at 1150 Hz. Is it a harmonic? Answer. No: 1150/199 ≈ 5.8 is not a whole number. It is a higher resonance of the cavity, a standing wave inside the bottle, which is not in a harmonic ratio with the Helmholtz resonance.

Further reading and links

  • We invite you to read the fundamental page Sound and resonance, where you will find the general principles of how a musical instrument works. Reading it will help you better appreciate the peculiarities of the instrument described on this page
  • The page on Helmholtz resonance further clarifies the sound production mechanism of the "instruments" on this page
"Physics, Waves, Music": a website about the physics of waves, acoustics of musical instruments, musical scales, harmony and music.