Misplaced Pages

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36-403: For symmetric periodic waves, like sine waves or triangle waves , peak amplitude and semi amplitude are the same. In audio system measurements , telecommunications and others where the measurand is a signal that swings above and below a reference value but is not sinusoidal , peak amplitude is often used. If the reference is zero, this is the maximum absolute value of the signal; if

72-471: 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

108-449: A zero at the origin of the complex frequency plane. The gain of its frequency response increases at a rate of +20  dB per decade of frequency (for root-power quantities), the same positive slope as a 1 order high-pass filter 's stopband , although a differentiator doesn't have a cutoff frequency or a flat passband . A n -order high-pass filter approximately applies the n time derivative of signals whose frequency band

144-471: A flat passband. A n -order low-pass filter approximately performs the n time integral of signals whose frequency band is significantly higher than the filter's cutoff frequency. Radio frequency Radio frequency ( RF ) is the oscillation rate of an alternating electric current or voltage or of a magnetic , electric or electromagnetic field or mechanical system in the frequency range from around 20  kHz to around 300  GHz . This

180-532: A quarter cycle, the sine and cosine components , respectively. A sine wave represents a single frequency with no harmonics and is considered an acoustically pure tone . Adding sine waves of different frequencies results in a different waveform. Presence of higher harmonics in addition to the fundamental causes variation in the timbre , which is the reason why the same musical pitch played on different instruments sounds different. Sine waves of arbitrary phase and amplitude are called sinusoids and have

216-409: A single line. This could, for example, be considered the value of a wave along a wire. In two or three spatial dimensions, the same equation describes a travelling plane wave if position x {\displaystyle x} and wavenumber k {\displaystyle k} are interpreted as vectors, and their product as a dot product . For more complex waves such as the height of

252-447: A sum of sine waves of various frequencies, relative phases, and magnitudes. When any two sine waves of the same frequency (but arbitrary phase ) are linearly combined , the result is another sine wave of the same frequency; this property is unique among periodic waves. Conversely, if some phase is chosen as a zero reference, a sine wave of arbitrary phase can be written as the linear combination of two sine waves with phases of zero and

288-567: A transient loudness attack, decay, sustain, and release. With waveforms containing many overtones, complex transient timbres can be achieved by assigning each overtone to its own distinct transient amplitude envelope. Unfortunately, this has the effect of modulating the loudness of the sound as well. It makes more sense to separate loudness and harmonic quality to be parameters controlled independently of each other. To do so, harmonic amplitude envelopes are frame-by-frame normalized to become amplitude proportion envelopes, where at each time frame all

324-476: A water wave in a pond after a stone has been dropped in, more complex equations are needed. French mathematician Joseph Fourier discovered that sinusoidal waves can be summed as simple building blocks to approximate any periodic waveform, including square waves . These Fourier series are frequently used in signal processing and the statistical analysis of time series . The Fourier transform then extended Fourier series to handle general functions, and birthed

360-398: Is dependent on waveform . If the wave shape being measured is greatly different from a sine wave, the relationship between RMS and average value changes. True RMS-responding meters were used in radio frequency measurements, where instruments measured the heating effect in a resistor to measure a current. The advent of microprocessor -controlled meters capable of calculating RMS by sampling

396-399: Is important in the search for exoplanets (see Doppler spectroscopy ). In general, the use of peak amplitude is simple and unambiguous only for symmetric periodic waves, like a sine wave, a square wave, or a triangle wave. For an asymmetric wave (periodic pulses in one direction, for example), the peak amplitude becomes ambiguous. This is because the value is different depending on whether

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432-416: Is no longer amplitude since there is the possibility that a constant ( DC component ) is included in the measurement. Peak-to-peak amplitude (abbreviated p–p or PtP or PtoP ) is the change between peak (highest amplitude value) and trough (lowest amplitude value, which can be negative). With appropriate circuitry, peak-to-peak amplitudes of electric oscillations can be measured by meters or by viewing

468-450: Is proportional to the square of the RMS amplitude (and not, in general, to the square of the peak amplitude). For alternating current electric power , the universal practice is to specify RMS values of a sinusoidal waveform. One property of root mean square voltages and currents is that they produce the same heating effect as a direct current in a given resistance. The peak-to-peak value

504-439: Is related to amplitude and intensity and is one of the most salient qualities of a sound, although in general sounds it can be recognized independently of amplitude . The square of the amplitude is proportional to the intensity of the wave. For electromagnetic radiation , the amplitude of a photon corresponds to the changes in the electric field of the wave. However, radio signals may be carried by electromagnetic radiation;

540-480: Is represented by a scalar. Other sounds can have percussive amplitude envelopes featuring an abrupt onset followed by an immediate exponential decay. Percussive amplitude envelopes are characteristic of various impact sounds: two wine glasses clinking together, hitting a drum, slamming a door, etc. where the amplitude is transient and must be represented as either a continuous function or a discrete vector. Percussive amplitude envelopes model many common sounds that have

576-606: Is roughly between the upper limit of audio frequencies and the lower limit of infrared frequencies, and also encompasses the microwave range. These are the frequencies at which energy from an oscillating current can radiate off a conductor into space as radio waves , so they are used in radio technology, among other uses. Different sources specify different upper and lower bounds for the frequency range. Electric currents that oscillate at radio frequencies ( RF currents ) have special properties not shared by direct current or lower audio frequency alternating current , such as

612-1181: Is significantly lower than the filter's cutoff frequency. Integrating any sinusoid with respect to time can be viewed as dividing its amplitude by its angular frequency and delaying it a quarter cycle: ∫ A sin ⁡ ( ω t + φ ) d t = − A ω cos ⁡ ( ω t + φ ) + C = − A ω sin ⁡ ( ω t + φ + π 2 ) + C = A ω sin ⁡ ( ω t + φ − π 2 ) + C . {\displaystyle {\begin{aligned}\int A\sin(\omega t+\varphi )dt&=-{\frac {A}{\omega }}\cos(\omega t+\varphi )+C\\&=-{\frac {A}{\omega }}\sin(\omega t+\varphi +{\tfrac {\pi }{2}})+C\\&={\frac {A}{\omega }}\sin(\omega t+\varphi -{\tfrac {\pi }{2}})+C\,.\end{aligned}}} The constant of integration C {\displaystyle C} will be zero if

648-438: Is used, for example, when choosing rectifiers for power supplies, or when estimating the maximum voltage that insulation must withstand. Some common voltmeters are calibrated for RMS amplitude, but respond to the average value of a rectified waveform. Many digital voltmeters and all moving coil meters are in this category. The RMS calibration is only correct for a sine wave input since the ratio between peak, average and RMS values

684-402: The bounds of integration is an integer multiple of the sinusoid's period. An integrator has a pole at the origin of the complex frequency plane. The gain of its frequency response falls off at a rate of -20 dB per decade of frequency (for root-power quantities), the same negative slope as a 1 order low-pass filter 's stopband, although an integrator doesn't have a cutoff frequency or

720-505: The square root of the mean over time of the square of the vertical distance of the graph from the rest state; i.e. the RMS of the AC waveform (with no DC component ). For complicated waveforms, especially non-repeating signals like noise, the RMS amplitude is usually used because it is both unambiguous and has physical significance. For example, the average power transmitted by an acoustic or electromagnetic wave or by an electrical signal

756-514: The 50 or 60 Hz current used in electrical power distribution . The radio spectrum of frequencies is divided into bands with conventional names designated by the International Telecommunication Union (ITU): Frequencies of 1 GHz and above are conventionally called microwave , while frequencies of 30 GHz and above are designated millimeter wave . More detailed band designations are given by

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792-433: The amplitude is a displacement . The amplitude of sound waves and audio signals (which relates to the volume) conventionally refers to the amplitude of the air pressure in the wave, but sometimes the amplitude of the displacement (movements of the air or the diaphragm of a speaker ) is described. The logarithm of the amplitude squared is usually quoted in dB , so a null amplitude corresponds to − ∞  dB. Loudness

828-417: The amplitude of frequency - and phase -modulated waveform envelopes . In this simple wave equation The units of the amplitude depend on the type of wave, but are always in the same units as the oscillating variable. A more general representation of the wave equation is more complex, but the role of amplitude remains analogous to this simple case. For waves on a string , or in a medium such as water ,

864-522: The current proliferation of radio frequency wireless telecommunications devices such as cellphones . Medical applications of radio frequency (RF) energy, in the form of electromagnetic waves ( radio waves ) or electrical currents, have existed for over 125 years, and now include diathermy , hyperthermy treatment of cancer, electrosurgery scalpels used to cut and cauterize in operations, and radiofrequency ablation . Magnetic resonance imaging (MRI) uses radio frequency fields to generate images of

900-793: The field of Fourier analysis . Differentiating any sinusoid with respect to time can be viewed as multiplying its amplitude by its angular frequency and advancing it by a quarter cycle: d d t [ A sin ⁡ ( ω t + φ ) ] = A ω cos ⁡ ( ω t + φ ) = A ω sin ⁡ ( ω t + φ + π 2 ) . {\displaystyle {\begin{aligned}{\frac {d}{dt}}[A\sin(\omega t+\varphi )]&=A\omega \cos(\omega t+\varphi )\\&=A\omega \sin(\omega t+\varphi +{\tfrac {\pi }{2}})\,.\end{aligned}}} A differentiator has

936-403: The form: Since sine waves propagate without changing form in distributed linear systems , they are often used to analyze wave propagation . When two waves with the same amplitude and frequency traveling in opposite directions superpose each other, then a standing wave pattern is created. On a plucked string, the superimposing waves are the waves reflected from the fixed endpoints of

972-415: The general form: y ( t ) = A sin ⁡ ( ω t + φ ) = A sin ⁡ ( 2 π f t + φ ) {\displaystyle y(t)=A\sin(\omega t+\varphi )=A\sin(2\pi ft+\varphi )} where: Sinusoids that exist in both position and time also have: Depending on their direction of travel, they can take

1008-401: The harmonic amplitudes will add to 100% (or 1). This way, the main loudness-controlling envelope can be cleanly controlled. In Sound Recognition, max amplitude normalization can be used to help align the key harmonic features of 2 alike sounds, allowing similar timbres to be recognized independent of loudness. Sine wave A sine wave , sinusoidal wave , or sinusoid (symbol: ∿ ) is

1044-413: The human body. Radio Frequency or RF energy is also being used in devices that are being advertised for weight loss and fat removal. The possible effects RF might have on the body and whether RF can lead to fat reduction needs further study. Currently, there are devices such as trusculpt ID , Venus Bliss and many others utilizing this type of energy alongside heat to target fat pockets in certain areas of

1080-444: The intensity of the radiation ( amplitude modulation ) or the frequency of the radiation ( frequency modulation ) is oscillated and then the individual oscillations are varied (modulated) to produce the signal. Amplitude envelope refers to the changes in the amplitude of a sound over time, and is an influential property as it affects perception of timbre. A flat tone has a steady state amplitude that remains constant during time, which

1116-468: The maximum positive signal is measured relative to the mean, the maximum negative signal is measured relative to the mean, or the maximum positive signal is measured relative to the maximum negative signal (the peak-to-peak amplitude ) and then divided by two (the semi-amplitude ). In electrical engineering, the usual solution to this ambiguity is to measure the amplitude from a defined reference potential (such as ground or 0 V). Strictly speaking, this

Amplitude - Misplaced Pages Continue

1152-456: The reference is a mean value ( DC component ), the peak amplitude is the maximum absolute value of the difference from that reference. Semi-amplitude means half of the peak-to-peak amplitude. The majority of scientific literature employs the term amplitude or peak amplitude to mean semi-amplitude. It is the most widely used measure of orbital wobble in astronomy and the measurement of small radial velocity semi-amplitudes of nearby stars

1188-470: The standard IEEE letter- band frequency designations and the EU/NATO frequency designations. Radio frequencies are used in communication devices such as transmitters , receivers , computers , televisions , and mobile phones , to name a few. Radio frequencies are also applied in carrier current systems including telephony and control circuits. The MOS integrated circuit is the technology behind

1224-500: The string. The string's resonant frequencies are the string's only possible standing waves, which only occur for wavelengths that are twice the string's length (corresponding to the fundamental frequency ) and integer divisions of that (corresponding to higher harmonics). The earlier equation gives the displacement y {\displaystyle y} of the wave at a position x {\displaystyle x} at time t {\displaystyle t} along

1260-441: The waveform has made true RMS measurement commonplace. In telecommunications, pulse amplitude is the magnitude of a pulse parameter, such as the voltage level, current level, field intensity , or power level. Pulse amplitude is measured with respect to a specified reference and therefore should be modified by qualifiers, such as average , instantaneous , peak , or root-mean-square . Pulse amplitude also applies to

1296-410: The waveform on an oscilloscope . Peak-to-peak is a straightforward measurement on an oscilloscope, the peaks of the waveform being easily identified and measured against the graticule . This remains a common way of specifying amplitude, but sometimes other measures of amplitude are more appropriate. Root mean square (RMS) amplitude is used especially in electrical engineering : the RMS is defined as

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