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Free trigonometry worksheets, in PDF format, with solutions to download. Either open the file and print or download and save an electronic copy and use when needed. Worksheets with Trigonometry Questions Graph Trigonometric Functions
College Trigonometry » Trigonometry Course Outline College Trigonometry Course Outline Unit 1 – Prerequisites P.1 Real Numbers and Their Properties P.2 Solving Equations
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The signal velocity is the speed at which a wave carries information. It describes how quickly a message can be communicated (using any particular method) between two separated parties. Every signal velocity is always slower than (or equal to) the speed of a light pulse in a vacuum (by Special Relativity ). Signal velocity is usually equal to group velocity (the speed of a short "pulse" or of a wave-packet's middle or "envelope"). However, in a few special cases (e.g., media designed to amplify the front-most parts of a pulse and then attenuate the back section of the pulse), group velocity can exceed the speed of light in vacuum, while the signal velocity will still be less than or equal to the speed of light in vacuum. In electronic circuits, signal velocity is one member of a group of five closely related parameters.
In classical mechanics , linear momentum or translational momentum ( pl. momenta; SI unit kg m/s , or equivalently, N s ) is the product of the mass and velocity of an object. For example, a heavy truck moving fast has a large momentum—it takes a large and prolonged force to get the truck up to this speed, and it takes a large and prolonged force to bring it to a stop afterwards. If the truck were lighter, or moving more slowly, then it would have less momentum. Like velocity, linear momentum is a vector quantity, possessing a direction as well as a magnitude: Linear momentum is also a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change.
In physics , the kinetic energy of an object is the energy which it possesses due to its motion . [ 1 ] It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity . Having gained this energy during its acceleration , the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. In classical mechanics , the kinetic energy of a non-rotating object of mass m traveling at a speed v is ½ mv² . In relativistic mechanics , this is only a good approximation when v is much less than the speed of light . [ edit ] History and etymology
In physics, energy is an indirectly observed quantity which comes in many forms, such as kinetic energy , potential energy , radiant energy , and many others; which are listed in this summary article. This is a major topic in science and technology and this article gives an overview of its major aspects, and provides links to the many specific articles about energy in its different forms and contexts. The question "what is energy?" is difficult to answer in a simple, intuitive way, although energy can be rigorously defined in theoretical physics.
USSR postage stamp dedicated to Albert Einstein Special relativity ( SR , also known as the special theory of relativity or STR ) is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper " On the Electrodynamics of Moving Bodies ". [ 1 ] Galileo Galilei had already postulated that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames ), a principle now called Galileo's principle of relativity . Einstein extended this principle so that it accounted for the constant speed of light, [ 2 ] a phenomenon that had been recently observed in the Michelson-Morley experiment . He also postulated that it holds for all the laws of physics , including both the laws of mechanics and of electrodynamics , whatever they may be. [ 3 ]
The de Broglie relations redirect here. In quantum mechanics , the concept of matter waves or de Broglie waves ( pron.: / d ə ˈ b r ɔɪ / ) reflects the wave–particle duality of matter . The theory was proposed by Louis de Broglie in 1924 in his PhD thesis. [ 1 ] The de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle and is also called de Broglie wavelength .
Quantum mechanics (QM – also known as quantum physics , or quantum theory ) is a branch of physics dealing with physical phenomena at microscopic scales, where the action is on the order of the Planck constant . Quantum mechanics departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales. Quantum mechanics provides a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter .
In electronics and telecommunications , modulation is the process of varying one or more properties of a periodic waveform , called the carrier signal , with a modulating signal which typically contains information to be transmitted. This is done in a similar fashion to a musician modulating a tone (a periodic waveform) from a musical instrument by varying its volume , timing and pitch . The three key parameters of a periodic waveform are its amplitude ("volume"), its phase ("timing") and its frequency ("pitch"). Any of these properties can be modified in accordance with a low frequency signal to obtain the modulated signal. Typically a high-frequency sinusoid waveform is used as carrier signal , but a square wave pulse train may also be used. In telecommunications , modulation is the process of conveying a message signal, for example a digital bit stream or an analog audio signal, inside another signal that can be physically transmitted.
Frequency dispersion in groups of gravity waves on the surface of deep water. The red dot moves with the phase velocity , and the green dots propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity.
In optics the refractive index or index of refraction n of a substance ( optical medium ) is a dimensionless number that describes how light , or any other radiation , propagates through that medium. It is defined as where c is the speed of light in vacuum and v is the phase velocity in the substance. For example, the refractive index of water is 1.33, meaning that light travels 1.33 times as fast in vacuum as it does in water.
In optics , dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, [ 1 ] or alternatively when the group velocity depends on the frequency. Media having such a property are termed dispersive media . Dispersion is sometimes called chromatic dispersion to emphasize its wavelength-dependent nature, or group-velocity dispersion ( GVD ) to emphasize the role of the group velocity. Dispersion is most often described for light waves, but it may occur for any kind of wave that interacts with a medium or passes through an inhomogeneous geometry (e.g., a waveguide ), such as sound waves.