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waves cheatsheet

waves cheatsheet - = 2 π/k m ω Angular frequency We...

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Physics 218 Spring 2008 Waves Cheat Sheet Here is in one place all the nomenclature we use for waves. Recall that the one-dimensional wave equation is 2 y ( x, t ) ∂x 2 - 1 v 2 p 2 y ( x, t ) ∂t 2 = 0 , where x is the position, t is the time, and y ( x, t ) is the displacement from equilibrium at a position x and a time t , and v p is the phase velocity of a single wave at a single frequency. A solution to the wave equation can come in the following forms: y ( x, t ) = A 1 cos( kx - ωt + φ ) = A 2 sin( kx - ωt + φ ) = A 3 exp[ i ( kx - ωt + φ )] . The table below gives an explanation, name, and relevant units for all the symbols in the above equations, and some additional ones that are related to them. Symbol Name Units A Amplitude. The symbol varies. varies k Wave number. k = 2 π/λ radians/m λ Wavelength. Length in space of one oscillation.
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Unformatted text preview: λ = 2 π/k m ω Angular frequency. We usually drop the “angular.” ω = 2 πν = 2 π/T radians/s ν Frequency. Usually, ω is more convenient. ν = ω/ 2 π = 1 /T 1/s T Period. Length in time of one oscillation. T = 1 /ν = 2 π/ω s φ Phase angle. radians v g Group velocity. v g = dω/dk m/s v p Phase velocity. Sometimes c is used. v p = ω/k m/s Beware in particular of the frequent misuse of “angular frequency” as frequency. I give above ν , the frequency, T , the period, and λ , the wavelength, though we don’t often talk about them, as they are more familiar in everyday usage. 1...
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