Banded Waveguides Synthesis is a physical modeling synthesis method to simulate sounds of dispersive sounding objects, or objects with strongly inharmonicresonantfrequencies efficiently. It can be used to model the sound of instruments based on elastic solids such as vibraphone and marimba bars, singing bowls and bells. It can also be used for other instruments with inharmonic partials, such as membranes or plates. For example, simulations of tabla drums and cymbals have been implemented using this method. Because banded waveguides retain the dynamics of the system, complex non-linear excitations can be implemented. The method was originally invented in 1999 by Georg Essl and Perry Cook to synthesize the sound of bowedvibraphone bars.[1]
In the case of the standard one-dimensional wave equation disturbances of all frequencies travel with the same constant speed . In dispersive media, the traveling speed of disturbances depends on their frequency and we get where is the frequency of the disturbance. Many physical systems are dispersive, for example the elastic beams described by the Euler–Bernoulli beam equation where is a material constant.
Banded waveguides model dispersive behavior by splitting the propagation of disturbances into frequency bands. Each frequency band is modeled using a band-limited version of the standard digital waveguide method. Each frequency band is tuned to the resonantfrequencies of the sounding object to be modeled to avoid any discretization error at the dominant and audible frequencies.[2]
Banded waveguide synthesis is implemented in most available sound synthesis libraries and programs such as:
Additive synthesis is a sound synthesis technique that creates timbre by adding sine waves together.
Frequency modulation synthesis is a form of sound synthesis whereby the frequency of a waveform is changed by modulating its frequency with a modulator. The (instantaneous) frequency of an oscillator is altered in accordance with the amplitude of a modulating signal.
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x: where k is a positive constant.
In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced rather than passing through.
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the fundamental frequency of a periodic signal. The fundamental frequency is also called the 1st harmonic; the other harmonics are known as higher harmonics. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a harmonic series.
Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration that matches its natural frequency. When this happens, the object or system absorbs energy from the external force and starts vibrating with a larger amplitude. Resonance can occur in various systems, such as mechanical, electrical, or acoustic systems, and it is often desirable in certain applications, such as musical instruments or radio receivers. However, resonance can also be detrimental, leading to excessive vibrations or even structural failure in some cases.
A waveguide is a structure that guides waves by restricting the transmission of energy to one direction. Common types of waveguides include acoustic waveguides which direct sound, optical waveguides which direct light, and radio-frequency waveguides which direct electromagnetic waves other than light like radio waves.
In music, inharmonicity is the degree to which the frequencies of overtones depart from whole multiples of the fundamental frequency.
A sine wave, sinusoidal wave, or sinusoid is a periodic wave whose waveform (shape) is the trigonometric sine function. In mechanics, as a linear motion over time, this is simple harmonic motion; as rotation, it corresponds to uniform circular motion. Sine waves occur often in physics, including wind waves, sound waves, and light waves, such as monochromatic radiation. In engineering, signal processing, and mathematics, Fourier analysis decomposes general functions into a sum of sine waves of various frequencies, relative phases, and magnitudes.
Digital waveguide synthesis is the synthesis of audio using a digital waveguide. Digital waveguides are efficient computational models for physical media through which acoustic waves propagate. For this reason, digital waveguides constitute a major part of most modern physical modeling synthesizers.
A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator can be either electromagnetic or mechanical. Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones. Another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of very precise frequency.
In electronic music, waveshaping is a type of distortion synthesis in which complex spectra are produced from simple tones by altering the shape of the waveforms.
A digital delay line is a discrete element in a digital filter, which allows a signal to be delayed by a number of samples. Delay lines are commonly used to delay audio signals feeding loudspeakers to compensate for the speed of sound in air, and to align video signals with accompanying audio, called audio-to-video synchronization. Delay lines may compensate for electronic processing latency so that multiple signals leave a device simultaneously despite having different pathways.
Lamb waves propagate in solid plates or spheres. They are elastic waves whose particle motion lies in the plane that contains the direction of wave propagation and the direction perpendicular to the plate. In 1917, the English mathematician Horace Lamb published his classic analysis and description of acoustic waves of this type. Their properties turned out to be quite complex. An infinite medium supports just two wave modes traveling at unique velocities; but plates support two infinite sets of Lamb wave modes, whose velocities depend on the relationship between wavelength and plate thickness.
An acoustic metamaterial, sonic crystal, or phononic crystal is a material designed to control, direct, and manipulate sound waves or phonons in gases, liquids, and solids. Sound wave control is accomplished through manipulating parameters such as the bulk modulus β, density ρ, and chirality. They can be engineered to either transmit, or trap and amplify sound waves at certain frequencies. In the latter case, the material is an acoustic resonator.
Resonant ultrasound spectroscopy (RUS) is a laboratory technique used in geology and material science to measure fundamental material properties involving elasticity. This technique relies on the fact that solid objects have natural frequencies at which they vibrate when mechanically excited. The natural frequency depends on the elasticity, size, and shape of the object—RUS exploits this property of solids to determine the elastic tensor of the material. The great advantage of this technique is that the entire elastic tensor is obtained from a single crystal sample in a single rapid measurement. At lower or more general frequencies, this method is known as acoustic resonance spectroscopy.
Georg Essl is an Austrian computer scientist and musician, who works in the areas of human-computer interaction, acoustics, mobile computing and mobile music. He is a visiting research professor at the College of Letters & Sciences at the University of Wisconsin–Milwaukee, and he is also affiliated with the Center for 21st Century Studies. Prior to that he was an assistant professor at the University of Michigan.
The numerical models of lasers and the most of nonlinear optical systems stem from Maxwell–Bloch equations (MBE). This full set of Partial Differential Equations includes Maxwell equations for electromagnetic field and semiclassical equations of the two-level atoms. For this reason the simplified theoretical approaches were developed for numerical simulation of laser beams formation and their propagation since the early years of laser era. The Slowly varying envelope approximation of MBE follows from the standard nonlinear wave equation with nonlinear polarization as a source:
Network synthesis is a design technique for linear electrical circuits. Synthesis starts from a prescribed impedance function of frequency or frequency response and then determines the possible networks that will produce the required response. The technique is to be compared to network analysis in which the response of a given circuit is calculated. Prior to network synthesis, only network analysis was available, but this requires that one already knows what form of circuit is to be analysed. There is no guarantee that the chosen circuit will be the closest possible match to the desired response, nor that the circuit is the simplest possible. Network synthesis directly addresses both these issues. Network synthesis has historically been concerned with synthesising passive networks, but is not limited to such circuits.
Critical embankment velocity or critical speed, in transportation engineering, is the velocity value of the upper moving vehicle that causes the severe vibration of the embankment and the nearby ground. This concept and the prediction method was put forward by scholars in civil engineering communities before 1980 and stressed and exhaustively studied by Krylov in 1994 based on the Green function method and predicted more accurately using other methods in the following. When the vehicles such as high-speed trains or airplanes move approaching or beyond this critical velocity, the vibration magnitudes of vehicles and nearby ground increase rapidly and possibly lead to the damage to the passengers and the neighboring residents. This relevant unexpected phenomenon is called the ground vibration boom from 1997 when it was observed in Sweden for the first time.
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