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Optics of Moving Sources

Problem 5.236

A source emitting electromagnetic signals with proper frequency \(\omega_{0}=3.0 \cdot 10^{10} \mathrm{~s}^{-1}\) moves at a constant velocity \(v\) \(=0.80 c\) along a straight line separated from a stationary observer \(P\) by a distance \(l\) (Fig. 5.37 ). Find the frequency of the signals perceived by the observer at the moment when (a) the source is at the point \(O\); (b) the observer sees it at the point \(O\).

Reveal Answer
5.236.( a) ω=ω0/1−β2=5.0⋅1010 s−1;(b)ω=ω01−β2==1.8⋅1010 s−1.Here β=v/c.\begin{aligned} & 5.236 .\left(\right.\text { a) } \omega=\omega_{0} / \sqrt{1-\beta^{2}}=5.0 \cdot 10^{10} \mathrm{~s}^{-1} ;(b) \omega=\omega_{0} \sqrt{1-\beta^{2}}=\\ =& 1.8 \cdot 10^{10} \mathrm{~s}^{-1} . \text {Here } \beta=v / c . \end{aligned}
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