(a) $n^{'} = n\left( \frac{v}{v - v_{S}} \right) \Rightarrow \frac{n^{'}}{n} = \frac{v}{v - v_{S}} \Rightarrow \frac{v}{v - v_{S}} = 3 \Rightarrow v_{s} = \frac{2v}{3}$
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Ph.D. in Physics with 19+ years of teaching experience.