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Vibrating String
A vibration in a string is a wave. Resonance causes a vibrating string to produce a sound with constant frequency, i.e. constant pitch. If the length or tension of the string is correctly adjusted, the sound produced is a musical tone. Vibrating strings are the basis of string instruments such as guitars, cellos, and pianos. For an homogenous string, the motion is given by the wave equation. Wave The velocity of propagation of a wave in a string (v) is proportional to the square root of the force of tension of the string (T) and inversely proportional to the square root of the linear density (\mu) of the string: v = \sqrt. This relationship was discovered by Vincenzo Galilei in the late 1500s. Derivation Source: Let \Delta x be the length of a piece of string, m its mass, and \mu its linear density. If angles \alpha and \beta are small, then the horizontal components of tension on either side can both be approximated by a constant T, for which the net horizontal for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Standing Waves On A String
Standing, also referred to as orthostasis, is a position in which the body is held in an upright (orthostatic) position and supported only by the feet. Although seemingly static, the body rocks slightly back and forth from the ankle in the sagittal plane, which bisects the body into right and left sides. The sway of quiet standing is often likened to the motion of an inverted pendulum. Standing at attention is a military standing posture, as is stand at ease, but these terms are also used in military-style organisations and in some professions which involve standing, such as modeling. ''At ease'' refers to the classic military position of standing with legs slightly apart, not in as formal or regimented a pose as standing at attention. In modeling, ''model at ease'' refers to the model standing with one leg straight, with the majority of the weight on it, and the other leg tucked over and slightly around. There may be a time when a person is standing, where they lose contro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Length
Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most systems of measurement a Base unit (measurement), base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system, the base unit for length is the metre. Length is commonly understood to mean the most extended size, dimension of a fixed object. However, this is not always the case and may depend on the position the object is in. Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, width, breadth, and depth. ''Height'' is used when there is a base from which vertical measurements can be taken. ''Width'' and ''breadth'' usually refer to a shorter dimension than ''length''. ''Depth'' is used for the measure of a third dimension. Length is the measure of one spatial dimension, whereas area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Television
Television (TV) is a telecommunication medium for transmitting moving images and sound. Additionally, the term can refer to a physical television set rather than the medium of transmission. Television is a mass medium for advertising, entertainment, news, and sports. The medium is capable of more than "radio broadcasting", which refers to an audio signal sent to radio receivers. Television became available in crude experimental forms in the 1920s, but only after several years of further development was the new technology marketed to consumers. After World War II, an improved form of black-and-white television broadcasting became popular in the United Kingdom and the United States, and television sets became commonplace in homes, businesses, and institutions. During the 1950s, television was the primary medium for influencing public opinion.Diggs-Brown, Barbara (2011''Strategic Public Relations: Audience Focused Practice''p. 48 In the mid-1960s, color broadcasting was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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CRT Screen
A cathode-ray tube (CRT) is a vacuum tube containing one or more electron guns, which emit electron beams that are manipulated to display images on a phosphorescent screen. The images may represent electrical waveforms on an oscilloscope, a Film frame, frame of video on an Analog television, analog television set (TV), Digital imaging, digital raster graphics on a computer monitor, or other phenomena like radar targets. A CRT in a TV is commonly called a picture tube. CRTs have also been Williams tube, used as memory devices, in which case the screen is not intended to be visible to an observer. The term ''cathode ray'' was used to describe electron beams when they were first discovered, before it was understood that what was emitted from the cathode was a beam of electrons. In CRT TVs and computer monitors, the entire front area of the tube is scanned repeatedly and systematically in a fixed pattern called a raster scan, raster. In color devices, an image is produced by con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Waveforms
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electronics'', 2nd ed., , CRC Press, 2002, p. 62 '' Periodic waveforms'' repeat regularly at a constant period. The term can also be used for non-periodic or aperiodic signals, like chirps and pulses. In electronics, the term is usually applied to time-varying voltages, currents, or electromagnetic fields. In acoustics, it is usually applied to steady periodic sounds — variations of pressure in air or other media. In these cases, the waveform is an attribute that is independent of the frequency, amplitude, or phase shift of the signal. The waveform of an electrical signal can be visualized with an oscilloscope or any other device that can capture and plot its value at various times, with suitable scales in the time and value axes. The ele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Mersenne's Laws
Mersenne's laws are laws describing the frequency of oscillation of a stretched string or monochord, useful in musical tuning and musical instrument construction. Overview The equation was first proposed by French mathematician and music theorist Marin Mersenne in his 1636 work '' Harmonie universelle''.Mersenne, Marin (1636)''Harmonie universelle'' Cited in, '' Wolfram.com''. Mersenne's laws govern the construction and operation of string instruments, such as pianos and harps, which must accommodate the total tension force required to keep the strings at the proper pitch. Lower strings are thicker, thus having a greater mass per length. They typically have lower tension. Guitars are a familiar exception to this: string tensions are similar, for playability, so lower string pitch is largely achieved with increased mass per length. Higher-pitched strings typically are thinner, have higher tension, and may be shorter. "This result does not differ substantially from Galileo's, yet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Node (physics)
A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an antinode, a point where the amplitude of the standing wave is at maximum. These occur midway between the nodes. Explanation Standing waves result when two sinusoidal wave trains of the same frequency are moving in opposite directions in the same space and interfere with each other. They occur when waves are reflected at a boundary, such as sound waves reflected from a wall or electromagnetic waves reflected from the end of a transmission line, and particularly when waves are confined in a resonator at resonance, bouncing back and forth between two boundaries, such as in an organ pipe or guitar string. In a standing wave the nodes are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Fundamental Frequency
The fundamental frequency, often referred to simply as the ''fundamental'' (abbreviated as 0 or 1 ), is defined as the lowest frequency of a Periodic signal, periodic waveform. In music, the fundamental is the musical pitch (music), pitch of a note that is perceived as the lowest Harmonic series (music)#Partial, partial present. In terms of a superposition of Sine wave, sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between adjacent frequencies. In some contexts, the fundamental is usually abbreviated as 0, indicating the lowest frequency Zero-based numbering, counting from zero. In other contexts, it is more common to abbreviate it as 1, the first harmonic. (The second harmonic is then 2 = 2⋅1, etc.) According to Benward and Saker's ''Music: In Theory and Practice'': Explanation All sinusoidal and many non-sinusoidal waveforms repeat exactly over time – they are per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Wave Period
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. The interval of time between events is called the period. It is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times per minute (2 hertz), its period is one half of a second. Special definitions of frequency are used in certain contexts, such as the angular frequency in rotational or cyclical properties, when the rate of angular progress is measured. Spatial frequency is defined for properties that vary or cccur repeatedly in geometry or space. The unit of measurement of frequency in the International System of Units (SI) is the hertz, having the symbol Hz. Definitions and units For cyclical phenomena such as oscillations, waves, or for examples o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves), phase'' on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The multiplicative inverse, inverse of the wavelength is called the ''spatial frequency''. Wavelength is commonly designated by the Greek letter lambda (''λ''). For a modulated wave, ''wavelength'' may refer to the carrier wavelength of the signal. The term ''wavelength'' may also apply to the repeating envelope (mathematics), envelope of modulated waves or waves formed by Interference (wave propagation), interference of several sinusoids. Assuming a sinusoidal wave moving at a fixed phase velocity, wave speed, wavelength is inversely proportion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Speed
In kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a non-negative scalar quantity. Introduction of the speed/velocity terminology by Prof. Tait, in 1882. The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Speed is the magnitude of ''velocity'' (a vector), which indicates additionally the direction of motion. Speed has the dimensions of distance divided by time. The SI unit of speed is the metre per second (m/s), but the most common unit of speed in everyday usage is the kilometre per hour (km/h) or, in the US and the UK, miles per hour (mph). For air and marine travel, the knot is commonly used. The fastest possible speed at wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Small-angle Approximation
For small angles, the trigonometric functions sine, cosine, and tangent can be calculated with reasonable accuracy by the following simple approximations: : \begin \sin \theta &\approx \tan \theta \approx \theta, \\ mu\cos \theta &\approx 1 - \tfrac12\theta^2 \approx 1, \end provided the angle is measured in radians. Angles measured in degrees must first be converted to radians by multiplying them by . These approximations have a wide range of uses in branches of physics and engineering, including mechanics, electromagnetism, optics, cartography, astronomy, and computer science. One reason for this is that they can greatly simplify differential equations that do not need to be answered with absolute precision. There are a number of ways to demonstrate the validity of the small-angle approximations. The most direct method is to truncate the Maclaurin series for each of the trigonometric functions. Depending on the order of the approximation, \textstyle \cos \theta is approxi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |