Acoustics

I5 Sound instruments

Manometric investigations of vibrating air columns

The presence of nodes and bulges in a sounding air column can be made visible by various methods: First of all, by the manometric flames of Karl Rudolf König 1832-1901 1862. Their applicability rests on the manometric capsule (Fig. 335) - an enclosed chamber a, the volume of which can be increased or reduced. Gas enters it through the tube b and leaves by the tube c. The wall AB is a very fine rubber membrane. If the air outside the chamber (on the left hand side of AB) is compressed, the membrane is vaulted inwards, if it is rarefied, outwards. In other words: Compression of the external air reduces the volume of the chamber a, condensation increases it. The pressure, at which the gas leaves the chamber, is increased in the first case, decreased in the second case, so that the length of the flame c becomes larger or smaller. If condensation and rarefaction follows each other , the flame jerks up and down. If you sing through a speaking trumpet (Fig. 336) against the membrane, you see how the flame, which initially was small and hardly visible, lengthens, but does not seem to reduce its length again. The long and short flames interchange so quickly, that the eye cannot separate them from each other. In order to to be able to see the differences, you are shown the images of the successive flames in a mirror which is moved so fast that every new image is seen at another location of the mirror, that is, the images of the flames are seen simultaneously, but side by side, that is, they are separated from each other (Wheatstone 1802-1875 1834).

You use as a mirror the reflecting surface of a prism (Fig. 336), which can be rotated about a vertical axis. If the mirror is rotated sufficiently fast, you see in it, as long as the membrane is at rest, a band of light, the width of which is equal to the height of the flame; however, as soon as a sound hits the membrane, you see a regularly notched band - the individual notches are the images of the flame (Fig. 337).

This method lets you examine the oscillations in pipes; you can show thus that the density of the air changes strongly at the nodes, not at all at the bulges and that the nodes change their locations (Figs. 332, 333), depending on whether the air column sounds its base tone or an overtone. Following König, you employ normally an open organ pipe (Fig. 338), which you activate once to give its base tone, another time to give its octave. In the first case (Fig. 338a), there is only one node - at the centre of the tube. For this purpose, you fit a capsule a into the wall of the tube, that is, you drill a hole into it and insert the capsule so that the membrane closes the hole air tight. In the second case (Fig. 338 b), that is, when the tube sounds the octave of the base tone, there are two nodes, which are located 1/4 of the length of the tube from its ends: You also install two capsules at the locations b and c. The gas is supplied to the capsules from the chamber d. If you light the gas and blow at the pipe so that it sounds its base tone, you see how the central flame (at a node) lengthens, the other two (between a node and a bulge) move only very little. In contrast, if you activate the pipe, so that it sounds the octave of its base tone, the central flame, which is now at a bulge, does not move, while the other two at the nodes move strongly.

If you now observe the flames in the rotating mirror, you see the jagged bands of light of Fig. 337. Since the base tone (1) has only half the number of oscillations as the octave (2), you see in the first case only half as many spikes as in the second case. The distances between the spikes represent the locations, at which the flame is small and almost cannot be seen.

A fast rotating mirror is also indispensable for the examination of timbre, of interference phenomena, of beats, etc. as well as of other fast processes such as the examination of the structure of electric sparks ( Feddersen 1857 being the first to do so); you see in the rotating mirror the apparently simple spark as to and fro light strokes, which follow each other at very small fractions of a second.

Dust figures, generated in vibrating air columns

Another method for the investigation of vibrations in columns of air is due to Kundt: It displays the nodes and hence allows to measure the wave length in a tube and thereby also velocities of sound and moduli of elasticity. In Fig. 339, G is a glass tube (at least 25 mm diameter), inside which the air tight piston H can be moved. Along the inside of the tube, lycopodium or cork powder is spread uniformly. The bar S extends into the tube; it is held fixed at its centre; rubbed longitudinally, it gives its base tone. You change the length of the air column by shifting H so that it resonates strongly with the tone of the bar. (In order to transmit strongly the oscillations of the bar, its end can be widened by a disk of cork.) The powder then forms Kundt's dust figures (Fig. 339), counter pieces to Chladni's figures, in the form of cross ribs and starlike patterns at the nodal points. Since any neighbouring nodes delimit half a wave, you can measure the wave length.

In addition, you can also measure the ratio of the velocities of propagation of sound in the bar and the air column; if the air in the tube is replaced by a gas, also the velocity of a gas. You know that v = l ˇ n and this time there are the two equations

vbar = lbar ˇ nbar , vair = lair ˇ nair , whence vbar/vair = lbar/lair.

n is cancelled, because the tones of the air column and the bar are the same. The wave length in air is known: It can be measured in Kundt's tube; the wave length of the bar is also known: It is twice the length of S. Hence we find the two velocities in the bar and in the air together, but that in air is known, whence follows that in the bar.

Dust figures, generated in vibrating air columns

Naturally, it is impossible to make air columns vibrate with the same apparatus which is used for solids with real points of attack. Indeed they are tuned almost exclusively by resonance. If you hold a tuning fork in front of the opening of the tube, the length of which is in the corresponding ratio to the wave length of the tone of the tuning fork, the column will sound. The chamber tone a1 corresponds to a wave of 786 mm, to an open tube, which is half as long (393 mm) and to a covered tube 196.5 mm long. Each of them gives this tone, if you hold a sounding tuning fork to the open end.

The same fork also causes sounding of 2-, 3-, 4- as long open tubes and of 3-, 5-, 7-ˇˇˇ times as long covered tubes, but then obtains the corresponding overtones of the corresponding base tones. The ratio of the sounding air column length to the wave length of the tone of the tuning fork is displayed clearly, if you hold the sounding fork over a measuring cylinder and change the air column in it by changing the level of the fluid. At a certain length of the air column, you will hear the tone very clearly. It is very convenient to change the length of an air column by dipping a tube with open ends (and a diameter of about 4 cm) vertically into a container with water and hold the tuning fork to the open end. As the air column is lengthened and shortened, it sounds in resonance when it has the corresponding length.

Moreover, you can make columns of air oscillate by blowing at them,when their oscillation is also due to resonance. This is the established way for excitation of the air columns in wind instruments (flute, oboe, etc.). For this purpose, the tube is given a mouth piece; the tube is then called a pipe, depending on its mouth piece, a lip pipe or a tongue pipe. A representative of lip pipes - which include flutes and the majority of organ pipes - is the lip pipe of the organ. Fig. 340 presents a bi-sected four corner organ pipe. The air column in it is blown at by forcing an air stream through the canal h - in an organ, by bellows, in a flute by mouth. The air stream reaches the chamber K and escapes like a band through the gap s.

You can convince yourself of the form, which a gap gives to an air stream, and indeed for quite a large distance, by letting gas escape out of a Bunsen burner through a gap and lighting it.) The band of air impacts against the edge of the lip, which is parallel to the gap, and oscillates - following the latest theory of Wachsmuth - like a swinging tongue (Fig. 341) to and fro around the lip This swinging is connected with the formation of periodic vortices at the sides of the lamella [Krüger]. According to the earliest theory (Strouhal), which is supposed to have been replaced, the band of air provokes by friction at the lip a buzzing noise; it consists of a mixture of different height tones including the base tone of the organ pipe, by resonance with which the organ pipe sounds.

Among the musical instruments, only the flutes - their mouth piece is similar to that of the organ pipe - and a number of organ pipes represent the majority of lip pipes. Their mode of construction demands that their strength of sound remains almost unaltered. If you drive an air stream through the gap more strongly, its tone rises, essentially because the higher overtones then predominate and overcome the base tone. Hence you cannot strengthen or weaken the tone of an organ pipe by making the bellows work harder, but only by increasing or reducing mechanically the number of sounding pipes (combined in groups, they are called registers) and use of pipes, which have a sharper or softer timbre.

In tongue pipes, the pipe, or more accurately, the tube is unimportant and the tongue most important. Like a siren, it cuts up the blown air stream into air bursts, which follow one another in equally large, very small intervals. However, this pipe achieves it in a different manner from a siren. The air flows through the tongue mechanism through the same opening which is intermittently opened and closed by an oscillating strip, the tongue, which is installed in the opening like a hinged door.

The tongue is a very thin elastic lamella, which once it is displaced from its equilibrium position oscillates due to its elasticity. Fig. 341 shows its simplest form, the tongue of the organ tongue, harmonica, harmonium, chamber tone pipe. (It yields a hardly audible tone, for example, if it is stroked by the bow of a violin - this is a proof that what you hear are not the oscillations of the tongue.) The plate aa has a rectangular slot. The air flows through it; the measurements of the tongue agree with it, so that as it vibrates inwards at a certain position it closes it completely. In its position of rest, because it is somewhat bent, the tongue leaves the gap open. If you send through this instrument air by taking it between your lips - turning the upwards bent end of the tongue towards you mouth and blow into it - you hear a tone, the timbre of which is like that of a mouth organ. (You obtain the tone also by taking the tongue between your lips - the bent up end outwards - and sucking air through it. Both positions are used simultaneously in the mouth harmonica and accordion. As the flow of air impacts the tongue, it is deflected from its position of rest and due to its elasticity begins to oscillate . However, since the tongue then closes the gap completely in a certain position, it cuts up the flow into intermittent blows, which follow one another at the rate of the vibrations of the tongue. These blows generate the sensing of sound. As a rule, the tongue is a metal foil or a very elastic strip of wood (clarinet, oboe, bassoon).

In wind instruments, the flow of air passes through the tongue - an essential part of the mouth piece - into a tube, the mouth piece, - and thus, by entering in bursts, sets the air inside into oscillations; this occurs in all wooden and metal wind instruments of the orchestra (except the flute, which is a lip pipe). Certain instruments - harmonium, harmonica, chamber tone pipe - employ a tongue without a mouth piece. A mouth piece complicates the conditions of vibrations. It contains an air column; such a column, when blown at, gives a base tone and certain overtones, the heights of which dependon the length of the tube. This air column is then blown at through a mouth piece with a tongue; however, the tongue oscillates through its own elasticity, that is, has its own vibration period. If it coincides initially with that of the air column, that is, if the eigen tone of the tongue coincides with the base tone or an overtone of the tube - you only have to give the tube the length corresponding to the eigen tone of the tongue - - the pipe, when blown at, will give this tone.

If the two periods differ, the oscillations of the tongue and the air make a compromise, the tongue being decisive. However, it must not be a metal tongue as in the organ and harmonium. The periods of these comparatively heavy and stiff tongues are hardly affected by the oscillations of air columns. They are therefore only employed when each tone has its own tongue (as a string in a piano), indeed, in a harmonium without mouth piece or in the organ with a mouth piece, the length of which is adjusted to the tone of the tongue. Fig. 342 shows an organ tongue pipe. The air enters from the bellows through the tube h into the chamber K, from which it can only escape through the gap between the tongue z and the groove r. In the process, the tongue z oscillates, closes and opens intermittently the slot.

A tongue pipe with a tongue, which allows to produce a whole sequence of tones, is shown in Fig.343, the mouth piece of a clarinet - z is the tongue. Between it and the wall of the tube rs is a small slot, through which the air enters from the mouth into the tube. Depending on whether the column of air oscillates as a whole or, if one of the holes at its side is opened, partially, the tube yields another tone. The tongue is so flexible, that it always adjusts its rate of oscillation to that of the air column.

Singing flame

You can also cause the air in an open tube to sound by means of heat, especially a flame of hydrogen or domestic gas in a tube (Fig. 344); if the tube is suitably dimensioned, the flame can even be very strong. (singing flame of Higgins 1777).

According toTyndall, the sound is caused in the first place by friction at the edge of the burner. The sound of the tube is then, as in the case of lip pipes, a resonance phenomenon. (When gas escapes from a narrow opening , especially at high pressure, it tends to rush. You can hear this when domestic gas escapes!). In the rotating mirror of Fig. 336, you can observe that that the flame oscillates strongly while the tube sounds. Since obviously the vibrations cannot be separated from the oscillations of the air column or better, from the changes of pressure due to compaction and rarefaction of the gas, you will guess that the tone does not arise when the flame is at a bulge of the oscillating air column, where the pressure does not change. In fact, the tone does not arise, when the flame is at an end of the tube (where there is always a bulge), but only when it is inside the tube. - It is possible to excite apart from the base tone of the air column the first overtones. Naturally, the flame must adjust its rate of oscillation to the oscillations of the air. In this respect, it behaves like a very compliant tongue and a membrane of König.

Larynx. Voice ("organ")

Our larynx is a tongue pipe of a special kind, its tongue is a double tongue like a membrane. Fig. 345 shows it in a very simple form: two rubber membranes, stretched tight over the bevelled ends of a tube b leaving a fine slot ss. If air is driven through it, they oscillate simultaneously outwards and inwards. When they move outwards and inwards, the slit becomes larger and smaller, respectively, and eventually closes. Thus, by closing and opening the slot, the oscillations of the membrane tongues cut up the passing air flow like in a siren into bursts, which follow one another quickly and give a sound.

Our vocal chords are the tongues of our larynx. They close the wind pipe , which corresponds to the tube in Fig. 345. The air is pushed out of the lungs through the wind pipe and the larynx. The different tone heights are caused by the larynx by changes in the tension of the vocal chords and the strength of the air flow. The slit between the vocal chords is called glottis. Every time a sound is made, the vocal chords approach each other, so that the glottis almost closes (they close it completely when you cough!). The glotis of an adult man is 2.0 - 2.4 cm long and opens maximally to 1.4 cm. In a laryngoscope (Manuel Garcia 1805-1906), you can see clearly how it widens and contracts. On an average, the vocal chords of an adult man are 1.5 cm long.

The air stream from the lung blows at the larynx and enters the mouth piece of the mouth and nose spaces. Regarding the sounds, which we make with the aid of the larynx and mouth piece, we will only discuss the vowels.

According to experiments by Helmholtz 1863, the vowels maintain for our ears their characteristic difference, even when they are sung by the same mouth at the same height and the same strength - that is, the difference can only lie with the timbre. Indeed, an investigation has shown that the different vowels, sung at a given height, contain beside the base tone different numbers of overtones at different strengths. It is decisive for the sound of a vowel that it arises from an interaction of the larynx and the mouth cavity in front of it. The mouth cavity (together with the nose and throat cavities) acts as resonator and reinforces from the mixture of base tone and overtones those, which lie closest to the eigen tone of the mouth cavity; these sound then strongly out of the mouth cavity. However, one forms one's mouth cavity differently for every vowel, because one opens more or less for each of them the mouth, but positions the tongue, gums and lips differently. Thus, it is for every vowel a different resonator - different in form and volume - which selectively reinforces the mixture of sounds. This is why every vowel leaves the mouth cavity with a different timbre. Fig. 346 shows the different forms of the mouth cavity, which arise during sounding of the vowels a, u and i; they are constantly characteristic for every person. They give it the characteristic timbre, which we refer to as a peron's organ; even over years, it changes less than a person's face and makes itself known to our ears just as its face to our eyes. However, not all people have the same organ. The overtones, which, for example, characterize the vowel a of the person X, have therefore not quite the same Hertz number as those, which characterise the vowel a of the person Z. According to Ludimar Hermann 1838-1914, the overtones, which characterize a vowel lie therefore within a certain range of periods. This is shown clearly in Fig. 348 for the overtones of the vowel a, spoken by two different persons.

The ordinates display the strength (amplitude) of the overtones.The two records differ, because the organs of the two persons differed. However, they have in common a reinforcement zone of 800 to 1000 Hertz. Records like these are also obtained for consonants and noise of all kinds by the automatic sound analysis of Grützmacher 1927, an approach which works with the latest (in 1935!) electro-acoustic equipment (microphone, rectifier, damping-chain, amplifier, etc.). The table in Fig. 347 presents the characteristic ranges of formants for the vowels a, e, i, o and u.

Thus, the overtones, amplified by a given mouth cavity, are always the same for a given vowel. The heights of the overtones, which characterize the timbre of a vowel, therefore do not depend on the height of the base tone; indeed they have an absolute height. If one changes during intonation the base tone, the order number of such an overtone may change, but not its height. Helmholtz has expressed this conclusion as follows: "The sounds of vowels differ from the sounds of most of the other musical instruments essentially in that the strengths of their overtones depend not only on their Hertz numbers, but predominantly on the heights of their tones. For example, if I sing the vowel A on the note Es, the amplified sound b" is the 12th of the sound, but if I sing the same vowel on the note b', the 2nd tone of the sound is reinforced."

We can also let our lips act as tongues by pressing them tightly together and blowing air from the mouth cavity through them. They are then tightened, as you feel immediately. If the pressure in the mouth becomes so strong that it overcomes the tension, the lips are opened a little bit. The air exits, the pressure in the mouth cavity drops and the tension in the lips again closes the cavity. This interaction continues and decomposes the air flow into bursts. While doing so, you feel the accompanying buzzing of the lips as tickling. The lips also act as tongues, as one blows into brass instrument: Trumpets, trombones and bugles. They form the tone similarly to when you whistle with your mouth; obviously, the tongue and the teeth then participate.