 Solution

ID: past-exam-of-the-symmetry-and-relativity-course-of-the-university-of-oxford/2017/3/b/a/solution

Take the wave along positive

x

, so

k_{x} = ω / c

. A longitudinal boost

V = (v_{x}, 0, 0)

gives

ω^{'} = γ_{x} ω (1 - v_{x} / c) = ω \frac{1 - v _{x} / c}{1 + v _{x} / c} .

A receiver moving in the propagation direction measures a redshift. The same signed expression gives a blueshift when

v_{x} < 0

. If the original wave propagates along negative

x

instead, retain

k_{x} = - ω / c

in the general formula.

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