What is a wave? The one-dimensional wave equation
What is a wave? The one-dimensional wave equation
What is a wave? The one-dimensional wave equation
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2/3/14<strong>What</strong> about a harmonic <strong>wave</strong>?E = E 0cos k(x − ct);φ = k(x − ct)<strong>The</strong> argument of the cosine function represents the phase of the <strong>wave</strong>,ϕ, or the fraction of a complete cycle of the <strong>wave</strong>.€In-phase <strong>wave</strong>sLine of equal phase = <strong>wave</strong>front = contours of maximum fieldOut-of-phase<strong>wave</strong>s<strong>The</strong> Phase VelocityHow fast <strong>is</strong> the <strong>wave</strong> traveling?Velocity <strong>is</strong> a reference d<strong>is</strong>tancedivided by a reference time.<strong>The</strong> phase velocity <strong>is</strong> the <strong>wave</strong>length / period: v = λ / τ Since f = 1/τ :v = λ fIn terms of k, k = 2π / λ, andthe angular frequency, ω = 2π / τ, th<strong>is</strong> <strong>is</strong>:v = ω / k3
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