Doppler Shift | Primer on Geometric Algebra | David Hestenes

Doppler Shift

Previous section: Lorentz Contraction.

Next sectionLorentz Transformations.

A distant source with velocity V = γ (1 + v/c) emits light signals with frequency
′ = ω′ / 2π = 1 / t′  that are received with frequency  f = ω / 2π = 1 / t, as shown in the figure.

Exercise:
From the figure derive the equation

λ(X2 X1)  =  D − V ,

where λ is a scale factor and

D   ′ /  f

is the Doppler factor. Derive and discuss the result

$\Large{D\,\,\, = \,\,\,\frac{{f'}}{f}\,\,\, = \,\,\,\gamma \,\left( {1\,\, \pm \,\,v/c} \right)\,\,\, = \,\,\,\sqrt {\frac{{c \pm v}}{{c \mp v}}} \,\,\, = \,\,\,\frac{1}{{\gamma \,\left( {1\,\, \mp \,\,v/c} \right)}}}$

(
Click here for a solution to this exercise.)

Previous sectionLorentz Contraction.

Next section: Lorentz Transformations.