Question

A fixed source of sound emitting a certain frequency appears as $f_a$ when the observer is approaching the source with speed $v_0$ and $f_r$ when the observer recedes from the source with the same speed. The frequency of the source is

• A. $\frac{f_r+f_a}{2}$
• B. $\frac{f_r-f_a}{2}$
• C. $\sqrt{f_a{f}_r}$
• D. $\frac{2f_r{f}_a}{f_r+f_a}$

Answer 1

The correct option is A $\frac{f_r+f_a}{2}$

when observer is approaching

$f_a=\frac{v+v_o}{v}f$

when observer recedes

$f_b=\frac{v-v_o}{v}f$

$f_a+f_b=\frac{v+v_o}{v}f+\frac{v-v_o}{v}f=2f$

$f=\frac{f_a+f_b}{2}$