Amplitude: Difference between revisions

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Often the greatest magnitude at a given point of any spatially and temporally varying  physical quantity governed by a [[wave equation]]; can also mean the spatial part of a time-harmonic  [[wave]] function.<br/> For example, in the time-harmonic (or sinusoidal) [[scalar]] wave function with [[circular frequency]] &#x003c9;, <blockquote>[[File:ams2001glos-Ae17.gif|link=|center|ams2001glos-Ae17]]</blockquote> where &#x003c6;('''x''') is the (complex) amplitude of the wave, although the [[modulus]] of &#x003c6; also may be called  its amplitude. The (complex) amplitude of the scalar plane [[harmonic]] wave  <blockquote>[[File:ams2001glos-Ae18.gif|link=|center|ams2001glos-Ae18]]</blockquote> with [[wavenumber]] ''k'' and initial [[phase]] &#x003b8; is ''A'' exp(''ikx'' - ''i''&#x003b8;), the modulus of which, [[File:ams2001glos-Aex03.gif|link=|ams2001glos-Aex03]], is also  called the amplitude of the wave. In its most general sense, amplitude means extent or size. Thus  the amplitude of a wave is some measure of its size.
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== amplitude ==
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<div class="definition"><div class="short_definition">Often the greatest magnitude at a given point of any spatially and temporally varying  physical quantity governed by a [[wave equation]]; can also mean the spatial part of a time-harmonic  [[wave]] function.</div><br/> <div class="paragraph">For example, in the time-harmonic (or sinusoidal) [[scalar]] wave function with [[circular frequency]] &#x003c9;, <div class="display-formula"><blockquote>[[File:ams2001glos-Ae17.gif|link=|center|ams2001glos-Ae17]]</blockquote></div> where &#x003c6;('''x''') is the (complex) amplitude of the wave, although the [[modulus]] of &#x003c6; also may be called  its amplitude. The (complex) amplitude of the scalar plane [[harmonic]] wave  <div class="display-formula"><blockquote>[[File:ams2001glos-Ae18.gif|link=|center|ams2001glos-Ae18]]</blockquote></div> with [[wavenumber]] ''k'' and initial [[phase]] &#x003b8; is ''A'' exp(''ikx'' - ''i''&#x003b8;), the modulus of which, <div class="inline-formula">[[File:ams2001glos-Aex03.gif|link=|ams2001glos-Aex03]]</div>, is also  called the amplitude of the wave. In its most general sense, amplitude means extent or size. Thus  the amplitude of a wave is some measure of its size.</div><br/> </div>
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Revision as of 17:27, 7 November 2023

Often the greatest magnitude at a given point of any spatially and temporally varying physical quantity governed by a wave equation; can also mean the spatial part of a time-harmonic wave function.
For example, in the time-harmonic (or sinusoidal) scalar wave function with circular frequency ω,
ams2001glos-Ae17
where φ(x) is the (complex) amplitude of the wave, although the modulus of φ also may be called its amplitude. The (complex) amplitude of the scalar plane harmonic wave
ams2001glos-Ae18
with wavenumber k and initial phase θ is A exp(ikx - iθ), the modulus of which, ams2001glos-Aex03, is also called the amplitude of the wave. In its most general sense, amplitude means extent or size. Thus the amplitude of a wave is some measure of its size.


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