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In physics, sound energy is a form of energy that can be heard by living things. Only those waves that have a frequency of 16 Hz to 20 kHz are audible to humans. However, this range is an average and will slightly change from individual to individual.
The Hamiltonian of a system represents the total energy of the system; that is, the sum of the kinetic and potential energies of all particles associated with the system. . The Hamiltonian takes different forms and can be simplified in some cases by taking into account the concrete characteristics of the system under analysis, such as single or several particles in the system, interaction ...
The frequency of a sound is defined as the number of repetitions of its waveform per second, and is measured in hertz; frequency is inversely proportional to wavelength (in a medium of uniform propagation velocity, such as sound in air). The wavelength of a sound is the distance between any two consecutive matching points on the waveform.
It is the branch of science studying the psychological responses associated with sound including noise, speech, and music. Psychoacoustics is an interdisciplinary field including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science. [1]
A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics , this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field .
Hamiltonian may refer to: Hamiltonian mechanics , a function that represents the total energy of a system Hamiltonian (quantum mechanics) , an operator corresponding to the total energy of that system
for a system of particles at coordinates .The function is the system's Hamiltonian giving the system's energy. The solution of this equation is the action, , called Hamilton's principal function.
The Hamiltonian in this case is known as a sub-Riemannian Hamiltonian. Every such Hamiltonian uniquely determines the cometric, and vice versa. This implies that every sub-Riemannian manifold is uniquely determined by its sub-Riemannian Hamiltonian, and that the converse is true: every sub-Riemannian manifold has a unique sub-Riemannian Hamiltonian