Acoustic fundamentals: vibration and wave

The sensation of sound arises from periodic or non periodic fluctuations in the air pressure reaching our ear. Whether a balloon bursts or a human being sings, an air pressure pulse or a series of impulses spreads globally around the sound source.

Pulses of a sound transmitter (i.e. a string or a loudspeaker diaphragm) propagate as sound waves in the surrounding air. The air serves as a transmission medium. When a periodic vibration reaches our ear, we perceive it as sound or sound with definable pitch. When the impulses follow each other irregularly (non periodic vibration), we hear a noise. A single impulse is perceived as a click or pop. Simple periodic vibrations are what the acousticians call sound, complex composite vibrations, like the sounds of a musical instrument, as sound. Every note played on a musical instrument contains, in addition to the periodic vibrations, also noise components (bow stroke, attack or blowing noise), which make up its character. There are also sound mixtures (i.e. the sounds of bells) whose vibrations consist of mixed periodic parts: different pitches are mixed in the listening impression.

When creating a vibration, the sound source slightly deflects the surrounding air particles from their rest position, these "bump" the neighboring particle and move back again. The periodic motion of the sound transmitter alternately compresses and expands the surrounding air, and these periodic "density change waves" propagate globally in all directions until the energy of the momentum is consumed by the mass inertia of the air particles unless they are re-excited by the sound sender. The speed at which the impulses propagate in the air is the (constant) speed of sound of about 340 m per second. In the sound propagation temperature and moisture content of the air play a role. For example, the pitch of a wind instrument increases as the heated body of the instrument heats the air that is oscillating in the interior. (What is pitch?)

You can represent the periodic deflections of a vibration as a projection of a pendulum oscillation on a time track. The simplest model of a vibration is the only artificially produced wave-shaped sine wave. It is so named because it is the image of a simple sine function. The momentary state of the deflection at a certain point in time is called phase. The phase duration (period duration) is the time that the wave needs from one maximum deflection to the next. The number of oscillations per second is called frequency and measured in Hertz (Hz = oscillations per second): 440 oscillations per second (440 Hz) give the sound and doubling the frequency, the sound sounds an octave higher. (What is an octave?)

In a transverse wave, the vibrating particles move perpendicularly to the propagation direction of the wave (for example, a cork dancing on water waves). A wave in longitudinal movement where the particles oscillate parallel to the propagation direction (i.e. in the case of sound propagation in the air) is called longitudinal. (a piano has both components in its sound. the initial ping is transverse, and the sustained sound is logitudinal)

The lower limit of the audible range for the pitch sensation is about 20 Hz. Below this, the perception of a pitch at the listener becomes the sensation of individual impulses. The upper limit of the listening range is between 15 kHz and 20 kHz (20,000 Hz), depending on age.

From the instrument to the ear
Resonance, sound transmission, hearing

In most musical instruments, there is a a cavity or inner space that amplifies the vibration.  The strings of a violin pass their vibrations over the bridge to the corpus; The nose, mouth and throat of the singer radiate the vibrations generated in the larynx. These hollow bodies are called resonators. In them, the supplied vibrations are maintained and radiated (resonance); this effect is perceived as reinforcement and sound enhancement. The surrounding air or the cable in the electro-acoustic transmission act as a transmission medium. Not only the air, but also water or solid bodies (i.e. the concrete walls of a house) can act as a transmission medium. The denser the matter of the transmission medium, the better it conducts the sound. For sound insulation, therefore, materials with a loose structure such as felt or foam are used.

When listening, the outer ear catches the incoming sound and direct it to the eardrum, which picks up the vibrations. In the subsequent middle ear, three bones (hammer, anvil and stirrup) named after their shape are connected to the eardrum and guide the movement further to the inner ear. From there, the mechanical sound processes via snail, basilar membrane and the hair cells of the organ of Corti are converted into electrical currents (nerve stimuli) and transmitted to the brain, which interprets them as a pitch or sound impression. The spatial location of sound sources, z. For example, in stereophonic hearing, the brain performs by analyzing the small differences in time and volume with which sound information arrives at the left and right ear.

Intervals and natural tone series

The natural philosophers of antiquity discovered that musical pitches can be formed with string pitches in simple integer ratios: Comparing the pitch of a free-swinging and a string pinched at a certain point, so as to shortened it. The result is an interval between the two tones. If you attack z. For example, if the string descends right in the middle so that only the plucked half of the string can swing, this tone sounds an octave higher than the free-swinging string: The frequency ratio (frequency proportion) between the whole and the tapped string is 1: 2.

The pitches resulting from integer (harmonic) pitches of the string (pitch proportions to the fundamental 2/1, 3/1, 4/1, etc.) form the partial tone series (overtone, natural tone, harmonic series). Their intervals are getting smaller and smaller. The numerator of the fraction is at the same time the ordinal number of the respective partial tone: for example, the fifth partial tone has the frequency ratio 5/1 to this fundamental tone above a fundamental tone (counted as 1). The tones of the natural tone series also form integer frequency relations among themselves, which represent the respective interval between them. So there is between the 3rd and 4th natural tone the frequency ratio 3/4 (pure fourth).

Acoustics and music

Intervals and natural tone series

The natural philosophers of antiquity discovered that musical pitches can be formed with string pitches in simple integer ratios: Comparing the pitch of a free-swinging and a string tapped at a certain point, so shortened, results in an interval between the two tones. If you attack z. For example, the string is exactly in the middle, so n
is set. The same is true of a cycle of twelve pure fifths: the tone his, which is seven octaves higher, is higher than the tone c by the Pythagorean comma.


In the modern well-tempered mood one avoids the problem by artificially closing the series of intervals in the score by an enharmonic confusion to form a circle.

concert pitch


Glissandi with Open Harmonics

As a rule, today the 'a' is used to define the absolute pitch and to tune the instruments among themselves. The frequency of the voice was subject to great fluctuations in the history of music. In the Baroque period, for example, there were moods for chamber music and choral music, which were separated by a third. Since about 1700, a uniform pitch a 'prevailed, the frequency between 415 and 422 Hz, which was about a semitone lower than today's chamber pitch. Since then, the chamber sound has been rising steadily. In 1939 the chamber pitch a 'was fixed at 440 Hz; However, since then he has risen again by a few Hz, probably because musicians believe that the instruments sound more brilliant through a slightly higher mood. This is not a problem for the strings; however, in wind instruments there is little possibility of correcting the overall tuning without affecting the pitch purity of the instrument.


The French mathematician Jean Baptiste Fourier (1768-1830) found that all periodic wave forms can theoretically be reduced to sinusoidal vibrations (Fourier analysis) and that the sounds of musical instruments are always composed of the fundamental and integer multiples of the fundamental. Each musical instrument and each sung vowel has a specific frequency range in which the partial tones (harmonics, overtones, integer multiples) resonate particularly strongly, independently of the pitch of the fundamental tone. These typical frequency ranges for the tone of the instrument are called formant ranges. A two-dimensional representation of an instrument tone as a spectrum shows in a "snapshot" the expression of the overtones at a certain point in the sound history. 1/1, 2/1, 3/1, 4/1



Physically, the sound power can be expressed in watts per square meter. In acoustics, however, it is customary to specify different sound powers not in absolute values, but relative to a base value (reference level). These value ratios are expressed in the logarithmic unit of measure decibel (dB). When the level indicator of a tape recorder z. For example, 0 dB corresponds to the optimum signal strength tuned to the band. Signals below it do not use the full capacity of the tape; Signals above it are distorted.

The unit of measurement of the physically measurable sound power does not exactly correspond to the subjective perceived loudness of the signal, because the ear is differently sensitive in different frequency ranges. Sounds in the middle range are perceived as louder than sounds of the same sound level at the edges of the listening area. The Phonskala indicates the subjective volume perception independent of the pitch.

Room acoustics, echo

Every room in which music is made reflects the sound waves of the music. Musicians and audiences therefore hear a mixture of directly emitted sound returning from the walls with a slight delay. Depending on the nature of the room, the partial tones that influence the timbre are also reflected to different degrees. The calculation of such complicated processes is an important task of architects and acousticians in the construction of concert halls.


Insert a video of J Chilorio

Electronic sound processing

Analog music recording and editing

The basis of electronic sound processing are electro-acoustic transducers. These are devices that convert an air pressure fluctuation (sound) into electrical voltage fluctuations (eg the microphone) or conversely convert electrical voltage curves into mechanical movements, such as: B. the speaker diaphragm. After conversion to electrical voltage, the musical information can be edited in many ways: You can on a sound carrier, z. As the magnetic tape (tape) store, amplify or attenuate individual frequency ranges (filters, equalizers), mix the recorded signals with other information (mixer) or modulate them to a carrier frequency and transmit through the ether (broadcast). Since the voltage curve of the recorded on the sound carrier signal corresponds to the actual sound history, this technique is called analog.

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