The voice

Why do our voices sound so silly after we have inhaled helium from a balloon?

At a given gas pressure, only two factors affect the speed of sound in the gas: its adiabatic index ${\displaystyle \gamma }$, a constant summarising the thermodynamic properties of the gas, and its density. In particular, all else being equal, the speed of sound is inversely proportional to the square root of the density of the gas.

${\displaystyle v\propto {\frac {1}{\sqrt {\rho }}}}$

Helium has a density of about one seventh that of air and a somewhat higher adiabatic index (1.67 against 1.4). This means that the speed of sound in helium is about three times higher than in air (about 1000 m/s against 343 m/s).

When we produce a sound, the base frequency is determined by the vibration frequency of the vocal cords, and this does not change in air or in helium. However, the timbre of the voice is filtered by the cavities of the vocal apparatus (larynx, pharynx, nasal cavities and sinuses). These cavities have resonance frequencies determined by their size and by the speed of sound in the gas inhaled at the moment the voice is produced.

Consequently, inhaling helium raises the resonance frequencies of the cavities, and so does not make the voice higher in pitch, but makes its timbre thinner.

Of course, the opposite effect can be observed when a gas heavier than air is inhaled. You will find audio examples, videos and the discussion in the section on voice and the speed of sound.

Is it possible to sing two notes simultaneously?

Yes, double sounds can be obtained by means of various vocal techniques, some of which are not yet fully understood from the acoustic point of view. See the section devoted to this subject on the page on the human voice

Why is it that when a soprano sings in a high register, it is very difficult to distinguish the vowel sounds being sung?

The difference between vowels is ultimately a difference of timbre. We distinguish the various vowels from one another because their acoustic spectrum is different, that is, because they contain different amounts of energy at different frequencies. The way the energy produced by the vibration of the vocal cords is shared among the various frequencies is determined by the resonances of the cavities of the vocal apparatus, which are modified during phonation. These resonances are determined essentially by the volume of the various cavities, and lie in frequency ranges below 6000 Hz in adults. When a soprano sings high notes, however, the higher harmonics are more widely spaced, because the frequency of the fundamental is particularly high. Consequently, fewer harmonics fall within the range of the resonances of the vocal tract. Moreover, singing technique leads the singer to concentrate as much energy as possible on the fundamental, because this makes the sound easier to hear even at a distance. All this means that the information about the vowel being sung often becomes insufficient to distinguish it "by ear". Fortunately we do not listen only with our ears, but with the whole brain, which is perfectly able to reconstruct the missing part of the information if the context allows it (for example if the singer is singing in a language we know).

To listen to sound examples of the phenomenon and see their spectral analysis, see the section on vowels in singing.

Why are we able to distinguish vowel sounds if we pronounce them all with the same intonation?

The perceptual feature of sound that allows us to distinguish one vowel from another is ultimately its timbre, but we can also recognise the same vowel when it is pronounced by different voices, with different timbres. This is why phonologists and phonolinguists use the concept of formants. The formants of a sound do not coincide with its spectrum, but are a processing of it designed precisely to identify the phoneme pronounced, independently of the timbre and intonation of the voice that pronounced it.

To see audio examples and diagrams illustrating this point, go to the section devoted to vowels.

Wind instruments

Is it true that sound also reflects at the open end of a tube and not just at the closed end?

Yes, it is true. In fact, this reflection mechanism is the basis for the formation of notes of definite pitch in wind instruments. To understand how this happens, it is useful to compare it with the oscillations of a string, which are reflected along the string both when the end is fixed and when it is free. They are reflected because at the end of the string (whether fixed or free) there is an abrupt change in the properties of the medium, which forces the string at that point to an unchanging condition called a boundary condition.

When the string is ideal and fixed, the condition imposed is a node at the end, while if it is free the condition is an antinode. At first sight it seems that the medium in a sound tube does not change at the ends: there is air outside and air inside the tube. However, we must remember that a sound wave is not the transport of air, but the transport of a variation of pressure in the air. As far as pressure is concerned, being inside or outside a tube makes a big difference.

For example, at the open end of an ideal tube there can be no change in pressure, since at the point where the tube opens to the outside the pressure must always equal the external pressure. So the open end always behaves as a pressure node. Conversely, at the closed end the pressure variation will be at a maximum, because the air presses against an ideally unyielding wall. The closed end therefore behaves as a pressure antinode.

To visualise the phenomenon better, see the many animations on the page reflection in strings.

Why do the flute, clarinet and oboe play in completely different registers even though they are almost the exact same length (about 60 cm)?

The answer lies in the relations between the properties of conical and cylindrical pipes. For a detailed discussion see the page on the conical pipe. In short, remember that

• a conical pipe, whether half-open or open at both ends, has the same resonance frequencies as a cylindrical pipe open at both ends of the same effective length
• a half-open cylindrical pipe has a fundamental of half the frequency of a cylindrical pipe of the same length open at both ends and, moreover, lacks the even-order higher harmonics.

So the oboe has a conical body, and therefore produces a fundamental whose wavelength is twice the length of the instrument, the same as that of the flute, which is a cylinder open at both ends. The clarinet, instead, has a cylindrical bore, but the beating reed forces a pressure antinode at the mouthpiece, which makes it acoustically equivalent in every respect to a half-closed pipe. The clarinet therefore has a fundamental whose wavelength is about four times the length of the instrument, while the oboe and flute have a fundamental whose wavelength is twice the length of the instrument. In terms of frequency, therefore, the fundamental of the clarinet is about an octave lower than the fundamental of the flute and oboe.

It is not actually an exact octave, because the clarinet is not purely cylindrical, as it ends with a small conical bell.

This reasoning explains the difference in range between the instruments, while a description of the whole emitted spectrum is needed to account for the differences in timbre. One particularly evident feature of the clarinet's sound, however, can already be deduced from the observations above: the absence (or very strong attenuation) of the even-order harmonics. This means that the first higher harmonic of the fundamental is not the octave above, but the twelfth (an octave plus a perfect fifth).

How important is the material with which a wind instrument is made?

As far as sound production is concerned, the material of the body of a wind instrument is generally not as important as is commonly thought.

In wind instruments, in fact, the element set into vibration is directly the air, not the material of the bore. The vibration modes of a wooden or metal tube, moreover, have natural frequencies much higher than those of the air column they contain (see the discussion of the role of elasticity and density of the medium on the page on the speed of sound). The material plays a relatively important role only in the kind of friction it exerts on the air, and in any heat exchanges taking place in the first thin layer of air in contact with the walls.

The reason why, for example, a flute and a clarinet have very different ranges and timbres does not depend so much on the fact that the first has a metal body and the second a wooden one, but rather on the conditions at the ends (the first cylindrical and open at both ends, the second cylindrical but closed by the reed at one end), and on the different way the oscillations are induced in the bore (by a direct air jet in the first, by a reed in the second). See also the previous question, and the page on the conical pipe.

In string instruments, on the contrary, the vibrating element is a string, which in general does not itself couple well acoustically with the surrounding air, as shown by the fact that a plucked string produces a very weak sound unless it is supported by a suitable wooden resonating cavity. In this type of instrument the surrounding air is actually set into vibration by the body of the instrument, which is in turn excited by the string. So, in this class of instruments, the response characteristics of the body (and therefore also the material it is made of) are essential in determining the qualities of the resulting sound.

Is it possible to play two notes simultaneously with one wind instrument?

Every instrument (wind or not) produces many sounds simultaneously even when we hear only one. Indeed, every vibrating system, when excited, can oscillate in a large number of independent fundamental modes called normal modes. The illusion of hearing a single sound is ensured by our perceptual apparatus.

That said, it is true that there are particular conditions in which a player manages to excite two modes of the instrument particularly strongly. If the frequencies of these modes are not integer multiples, the sound produced is not easily "resolved" by our perceptual system, and so two distinct sounds appear to us.

To hear the examples and see their spectral resolution, see the sections

• double sounds on the clarinet,
• double sounds on the oboe

String instruments

Why do all string instruments have a hollow body?

In short: strings on their own can vibrate at precise frequencies, suitable for producing musical sound. However, their vibration is not easily transmitted to the surrounding air, so much so that a string on its own cannot be heard even a short distance from the source. The main function of the hollow body of string instruments is therefore to amplify the vibration of the string, turning it into radiated sound energy (sound) by exploiting the phenomenon of resonance. Put in another, more technical way, the sound box acts as an impedance matching device between the strings and the surrounding air.

• You will find an extended discussion of this point on the page sound and resonance
• See also the question How does the body of a string instrument make the sound produced by its strings louder?

How important is the material with which a bowed string instrument is made?

In string instruments, the vibrating and resonating element that selects the fundamental frequency emitted by the instrument (the note played) is a thin string of gut, steel or synthetic material. However, the sound necessarily reaches our ears through the air.

Yet it is easy to check that a string on its own, played without a hollow support, emits a very weak sound. The reason is that some physical characteristics of the string, such as its density and elasticity, are very different from those of the surrounding air, and this prevents the vibrations of the string from passing easily into the air (the page refraction in strings contains animations illustrating this point). In technical jargon we say that the string has an acoustic impedance very different from that of the air. If we want the oscillation of the string to be transmitted effectively to the air, we must match the two impedances by means of suitable connecting elements.

In bowed string instruments these connecting elements make up the body of the instrument. For example, in the violin family the strings rest on a bridge, which rests on a plate, which in turn forms the top of a hollow box. This whole body essentially serves to turn the oscillation of the strings into oscillation of the air as efficiently as possible and, therefore, to radiate the sound into the surrounding space.

Impedance matching in bowed strings is a rather complex process, and the elastic properties of the wood the box is made of clearly play a fundamental role. The quality of the material is therefore of primary importance for the good sound quality of these instruments.

Why is it that when we bow, pluck or strike the same string, we get different sounds even if it is the same note?

The note perceived from the vibration of a string corresponds in all three cases to the free vibration frequency of the string (called the fundamental frequency). However, the precise shape of the string during vibration is quite different in the three cases, because the initial conditions of the motion are different. Consequently, the sound produced in the three cases is not a pure sound, but the combination (the superposition) of many pure harmonic partials. What distinguishes the three sounds is the different intensity of each of these partials.

• For a more analytical description, with an animation of the motion, see the page on string instruments.
• For more information on the physics of strings see normal modes of a string, natural frequencies of a string

If we use harmonics to tune an instrument, will we always get good tuning?

• Not always. It depends on which harmonics are used, and on the range of the instrument.
• The only harmonic that guarantees perfect tuning is the octave, because the octave is consonant in all scales. However, if harmonics are used to tune different strings (as is often done on the guitar), the instrument will be tuned in perfect fourths and fifths, as in the Pythagorean scale. This scale provides optimal intonation only for a particular key and, consequently, the instrument will be in tune for Western music only in a limited number of chords, and may sound out of tune when modulating.
• While on the guitar this mistuning may not be particularly relevant for certain kinds of music, it is almost always intolerable on the piano. Because of the wider range of its notes, the mistuning can become progressively larger the further one moves from the central octave of the instrument. Natural harmonics can be used as a first approximation, but corrections that bring the scale back to some form of temperament are absolutely necessary in this case.
• This theoretical and practical problem has troubled the whole history of music. In the individual sections (e.g. natural scale, Pythagorean scale, etc.) you will find descriptions and information on the individual scales, while in the section comparisons between the different scales you will find listening examples to learn to hear the differences between the various tunings.

We can create natural and artificial harmonic sounds on a violin and a guitar. How are they different?

A sound that is harmonic with respect to a reference sound called the fundamental is a sound whose frequency is an integer multiple of the fundamental. On string instruments, the fundamental of a string corresponds to the sound obtained from its free oscillation, while harmonic sounds are obtained for string lengths equal to 1/2, 1/3, 1/4, 1/5, etc. of its length.

The difference between natural and artificial harmonics is the following:

• natural harmonics are obtained only with respect to the fundamentals of the open strings, by lightly touching the string at the positions indicated above. In this way a node is always imposed at the point of contact (the string cannot move there), but the excitation of the part of the string on either side of the node is not prevented. The waves travelling along the string can in fact propagate, giving a standing wave with a frequency of 2, 3, 4, 5, etc. times the fundamental.
• artificial harmonics are obtained with respect to any note the instrument can produce. On the violin they are obtained by selecting the desired note with the index finger of the left hand, and lightly touching the same string with the little finger at a fixed distance equal to 1/4 of the length of the vibrating part of the string. The first finger selects the fundamental, while the second imposes a node by light touch, corresponding to a harmonic two octaves above the fundamental. Moving the hand along the fingerboard, harmonics two octaves above all the other notes can be obtained.

For an illustration of the physics of the phenomenon see

• standing waves,
• reflection in strings,
• interference between reflected waves

To listen to sound examples see

• The dedicated section on the page on the violin

Why do we speak of a trumpet (or a tenor sax) in B flat, but not, for example, of a "violin in B flat"?

• The violin, like almost all other chordophones, has a set of several strings, each tuned to a different frequency, that is, corresponding to a different note. Starting from this set of fixed notes, all the other notes can be obtained by using the fingers to shorten the vibrating portion of the strings. Since a violin is not restricted to playing only a few fixed notes, there is no need to specify a note as the "origin of the reference system".
• The case of the trumpet (and of all the other brass instruments) is different: originally the trumpet had no valves. The fundamental note produced therefore corresponded to the first usable harmonic given the length of the tube, and the instrument could not produce sounds other than this one and its higher harmonics. So, for the trumpet there is a "privileged reference system", fixed by the length of its tube. Changing the size of the instrument, for example by lengthening the tube, meant obtaining an instrument completely different from the first, since it could produce a different set of notes. This also influenced musical notation, giving rise to transposing notation, and both the nomenclature and the notation have survived to the present day, even after the trumpet, with the invention of valves (in the early 19th century), acquired a piston mechanism that allows it to produce all the notes of the modern chromatic scale.
• For further information and examples see the page on the trumpet.

What is "Tartini's third sound" and how is it obtained?

Tartini's third sound is a sound perceived when two sufficiently intense sounds of suitable frequencies reach the ear simultaneously, but which does not correspond to any of the frequencies present in the original sounds. The conditions in which it is produced are easy to reproduce for a violinist (as Tartini was), who plays loudly and simultaneously a C₅ on the second string and an E₅ on the first string. The third sound in this case corresponds to a C₃. Its frequency is equal to the difference between the fundamentals of the two notes played.

For a more detailed illustration of the phenomenon, with audio examples and diagrams, see the section devoted to the third sound.

Why are some guitar strings made from nylon while others are covered with metal?

The guitar (like bowed string instruments) has a set of strings all of the same length, but each vibrating at a different frequency (tuning).

For a given string length, two elements determine its vibration frequency: its mass and its tension. For details see the page on the natural frequencies of a string. It is clear, therefore, that to obtain different notes the various strings of a guitar must differ in these parameters. Winding steel spirals around a nylon core serves precisely to increase the mass of the strings that must produce the lowest notes, so that their tension does not have to be increased excessively, which would subject the wooden structure to overly asymmetric stresses.

Percussion instruments

Why don't all percussion instruments produce a precise note the way string instruments do?

• No musical instrument, when excited, emits sound at a single frequency: each emits a whole "spectrum". This happens even when we perceive "a single precise note", and it characterises the timbre of each instrument. The perceived note is almost always the fundamental, that is, the note corresponding to the sound emitted at the lowest frequency. All the other sounds are called harmonics.
• Now, there is a fundamental difference between the spectrum of harmonic sounds emitted by a string or a sound tube, as in bowed strings and wind instruments, and those emitted by a plate or a membrane, as in many percussion instruments. The difference is that the harmonics emitted by a string or a tube all have frequencies that are integer multiples of the fundamental, while those emitted by a plate or a membrane do not.
• The physical explanation of this phenomenon is at the same time very important and fairly simple, and has to do only with the fact that a string or a sound tube are essentially one-dimensional systems, while a plate or a membrane are essentially two-dimensional.

• On the pages normal modes of a string, normal modes of a circular membrane and normal modes of a rectangular membrane you can find an illustration of the phenomenon, with animations and sounds to see and hear the various harmonics.
• Sound examples of instruments of indefinite pitch on the pages on the snare drum and other percussion instruments

Why are some percussion instruments, such as the timpani, tuned while others, such as the cymbals, are not?

• Clearly cymbals cannot be tuned, since all the physical parameters characterising them (size, shape, density of the material) are given and fixed. The only variable under the player's control is the way they are struck (point of contact, force and duration of the stroke, material of the beater, etc.). These parameters largely determine the acoustic result of the instrument, but even this is not enough to allow real tuning, simply because cymbals emit sound with a broad spectrum, and the partial components of this spectrum are not in harmonic ratios. For a mathematical treatment see natural frequencies of circular plates.

The timbral peculiarities of plates (cymbals, antique cymbals, gongs, tam-tams) are not, however, to be considered a limitation. On the contrary, the effects that can be obtained can be surprising (for an example see the sound of a tam-tam with its sonogram).

• Timpani are percussion instruments of the so-called membranophone class: the sound is obtained by striking with a special mallet a membrane (once of animal skin, now typically of mylar, a synthetic polymer) stretched over a hollow support similar to a large pot with a rounded bottom. Around the instrument there are tensioning rods that can be adjusted by means of a pedal under the base. These tensioners, controlled by the pedal, can change the tension of the membrane, up to doubling it. Elementary vibration theory (see for example the page on natural frequencies) shows that increasing the tension by a factor of 2 is equivalent to increasing the frequency of the fundamental by a factor of ${\displaystyle {\sqrt {2}}}$, which, in musical terms, corresponds to an interval of about an augmented fourth.

From the mathematical treatment we know that the circular membrane of the timpani shares with other membranes, with plates, and with all two-dimensional systems in general, the property of having higher harmonics at frequencies in non-integer ratios to the fundamental. The real question, then, is the following:

Why do timpani produce a sound of definite pitch?

The answer lies in the effect of the air: timpani are large instruments, and the air above the membrane outside the drum and, to a lesser extent, below the membrane inside the hollow body of the instrument, has the effect of lowering the frequencies of the modes, especially the lowest ones, until the ratios between some of them become very close to integers. Finally, the player helps to excite the harmonic modes by striking the membrane at a standard position about a quarter of the radius in from the edge.

Further details and sound examples on the page on the timpani.