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The concept of wavelength is most often applied to sinusoidal, or nearly sinusoidal, waves, because in a linear system the sinusoid is the unique shape that propagates with no shape change – just a phase change and potentially an amplitude change. [15] The wavelength (or alternatively wavenumber or wave vector) is a characterization of the ...
where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and v p is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a dispersion relation.
A modulated wave resulting from adding two sine waves of identical amplitude and nearly identical wavelength and frequency. A common situation resulting in an envelope function in both space x and time t is the superposition of two waves of almost the same wavelength and frequency: [2]
The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. [ 1 ] [ 2 ] [ 3 ] The Doppler effect is named after the physicist Christian Doppler , who described the phenomenon in 1842.
A is the amplitude of the wave (the peak magnitude of the oscillation), φ is a phase offset , ω is the (temporal) angular frequency of the wave, describing how many radians it traverses per unit of time, and related to the period T by the equation ω = 2 π T , {\displaystyle \omega ={\tfrac {2\pi }{T}},}
The de Broglie wavelength is the wavelength, λ, associated with a particle with momentum p through the Planck constant, h: =. Wave-like behavior of matter has been experimentally demonstrated, first for electrons in 1927 and for other elementary particles, neutral atoms and molecules in the years since.
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 the waveform on an oscilloscope .
A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency.