Physical aspects of flute playing (acoustics)

Tone/Sound

From a physical view, tones are oscillations. The pitch is defined by the frequency, the intensity by the amplitude.
The thing a musician calls a tone is for the physician a sound From the physical kind of view a tone is not one oscillation but a combination of severall partial tones it consists of.

The difference between tone/sound and noise lies in the orderliness of the oscillation. Regarding a noise, the oscillation of the air is very much irregular. For tones or sounds the movement of the air is very regular.

The sounds to be heard from an instrument are composed of harmonics or partials Every harmonic has an integral multiple frequency of the base tone. The mixture of those harmonics and the different amplitudes of the frequencies of all harmonics is characteristic for the sound of an instrument.

The flute sound has not so much harmonics as 80% of the energy are put in the base tone.

The different harmonics overlay each others and the resulting oscillation has an irregular shape with bumps and bends. This characteristic shape is called envelope.

Sound propagation

The sound needs a medium to travel from it's source to the receptor (for example the audience). In a vacuum no sound propagation is possible.

The velocity of sound depends on this tansport medium. For air in 20°C the sonic velocity is for example 343,8 m/s.

The influence of temperature on the velocity of sound and the compositon of the air is with regard of wind instruments leading to the rise of tuning with an instrument getting warmer. The instrument is getting warmer by the breath of the player regardless of the environmental temperature. Most obvious becomes this phenomenon when playing in cold churches and if there are longer breaks between the pieces to be played. In these cases the flute is getting warm only in the upper part of the instrument (head and upper end of middle joint). The temperature of the tube is degreasing down to the foot and thus the tones using a longer part (mostly deep tones) are in a deeper pitch than those using only a short part of the flute (for example a c2).

Resonance

Each instrument is a resonance body for the sounds produced by the musician. This means the oscillation of the instruments amplifies the sounds.

With string instruments the resonance is constructed to amplify the whole envelope of the instrument.

Regarding wind instruments they are so called air room resonators<, which amplify a sharply formed band of wavelengths. This band of wavelengths is adapted to the actually needed frequency by lengthening or truncation of the resonance body by keys, different lengths of pipes or slides.

How a flute tone is built

The flute sound is build by the oscillation of the air column inside the instrument. The movement of the air particles inside the flute is induced by the air blown across the edge of the mouth hole. This movement propagates across the tube of the flute down to the open end at the foot joint. Where the movement is recflected. The original oscillation build at the edge of the mouth hole is thus only amplified by the air inside the flute, which is only the resonance room for the oscillation in the head of the instrument.

Beside the flute the mouth of the player is a resonance room, too. This resonance room is divided in two parts by the tongue. thus the position of the tongue makes it possible to change the timbre of the tone.

Parameters of the tone building are thus the shape and dimension of the embouchure, where the air is coming out. Another factor is the velocity of the flowing air and the air impingement angle it strikes the edge of the mouth hole. The amount of air and the dimension of the open area of the mouth hole are other factors of tone building. In practice for higher tones the distance between the embouchure and the edge of the mouth hole are decreased and the opening of the lips is reduced. Thus the lips are a bit more pointed than for deeper tones.

As the movement of the air goes along the axes of the tube, it is called a longitudinal wave. The reflection leads to a standing wave, which is simply build by pressure differences along the axes of the tube. This wave goes down the tube and back again. And thus the wavelength of the open tube is twice its physical length (law of Bernoulli).

The only moving thing inside the tube of the flute ist the pressure difference. There is no airflow inside the flute. The blown air is only activating the vibration of the air.

The source of the sound is for the flute at the mouth hole and at the same time also at the first open finger hole. Thus the flute sounds always stereo. This effect is stronger for long tubes because of the bigger distance. This means a Piccolo sounds not that much stereo as a bass flute and a deep c is much more stereo sound than a middle c.

Intervals

The intervals are built from whole-number relations of the frequencies In equal temperament the ratio is not exactly met.

The discovery of these interrelations is attributed to the greek mathematician Pythagoras. Though it is possible that he learned these theories from the Babylonians.

Energy/Power

First I would like to cite some numbers about energy needed for flute playing to give a first impression about the scale.

Werner Richter gave 0,8% in his book "Bewusste Flötentechnik" as the physical efficiency (maximum output/loss) of the energy of the stream and the energy of the produced sound for an A (440 Hz) The second example is the sound power of a flute in the second octave. The power of the produced sound is at most 0,013 Watt. Compared to a weak electric bulb of 40 Watt the difference of magnitude. At the same time the last cited number shows how sensitive our hearing is.

The energy a musician spends to play a flute lies between 0,1 und 2,1 Watt, and depends on the intensity and pitch of the tone. Even a tuba can be played with energy in about this magnitude or with about nine times of this.

Hearing

The human sense of hearing covers frequencies from 20 Hz in the base range up to 20.000 Hz in the height. A human ear is so sensible to hear a sound of only 10-16 W/cm2. If the ear would be more sensible, we would hear the movements of the molecules in the air all the time.

Between the most gentle sounds we can hear and those sound so loud, that they are just before hurting the ear, lies a range of 12 orders of magnitude. The time needed to produce a signal through the hearing system is about two or three orders of magnitude shorter than the time needed by vision or Smelling.

The range of audible frequencies shrinks with age. Thus a person of 35 years hears only up to 15 kHz, someone aged 60 years only up to 5 kHz.

The form of the human auricle allows to detect the direction of the origin of a sound even if hearing only with one ear. Using both ears, the time difference of the arrival of the signal in both ears, is a further help to detect the origin of the sound. The construction of the middle ear using those tiny bones to connect with the inner ear, is used to amplify gentle sounds and to absorb very loud sounds to protect the inner ear.

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Author: Claudia Haider; Last updated 10.04.2013