• # question_answer A fixed source of souna emitting a certain frequency appears at ${{f}_{a}}$ when the observer is approaching the source with speed ${{v}_{0}}$ and frequency${{f}_{r}}$. when the observer recedes from the source with the same speed. The frequency of the source is :- A)  $\frac{{{f}_{a}}+{{f}_{r}}}{2}$ B)  $\frac{{{f}_{a}}-{{f}_{r}}}{2}$ C)  $\sqrt{{{f}_{a}}{{f}_{r}}}$ D)  $\frac{2{{f}_{r}}{{f}_{a}}}{{{f}_{r}}+{{f}_{a}}}$

${{f}_{a}}=\left[ \frac{v+{{v}_{0}}}{v} \right]f$  ?.(1)  ${{f}_{r}}=\left[ \frac{v-{{v}_{0}}}{v} \right]f$ ?.(2) $\frac{{{f}_{a}}}{f}=1+\frac{{{v}_{0}}}{v}$ and $\frac{{{f}_{r}}}{f}=1-\frac{{{v}_{0}}}{v}$ then $\frac{{{f}_{a}}}{f}+\frac{{{f}_{r}}}{f}=2\Rightarrow f=\frac{{{f}_{a}}+{{f}_{r}}}{2}$