Two identical sound sources emit waves of frequency $f$. An observer moves along the line joining them with a constant velocity $v$. What is the beat frequency heard by the observer?

Solution

1. The observer moves toward one source and away from the other with velocity $v$, where $c$ is the speed of sound.
2. The frequency heard from the source being approached is $f_1=f(c+v)/c$.
3. The frequency heard from the source being moved away from is $f_2=f(c-v)/c$.
4. The beat frequency is the difference $$\begin{array}{rl}|f_1-f_2|& =|f(c+v)/c-f(c-v)/c|\\ & =2fv/c\end{array}$$.
5. Hence the answer is (A).