Two whistles $A$ and $B$ have frequencies $660\text{ Hz}$ and $590\text{ Hz}$ respectively. An observer is…
Two whistles $A$ and $B$ have frequencies $660\text{ Hz}$ and $590\text{ Hz}$ respectively. An observer is standing in the middle of line joining the two sources. Source $B$ and observer are moving towards right with velocity $30\text{ ms}^{-1}$ and $A$ is standing to the left side. If the velocity of sound in air is $300\text{ ms}^{-1}$. The number of beats per second listened by the observer is
8
6
4
2
Solution
There is no relative motion between $O$ and $B$. Hence,
(Diagram showing observer $O$ moving right at $30\text{ ms}^{-1}$ and listener $B$ moving right at $30\text{ ms}^{-1}$)
$f_B' = f_B = 590\text{ Hz}$
But $f_A' = f_A \left(\frac{v - v_o}{v}\right) = 660 \left(\frac{300 - 30}{300}\right) = 594\text{ Hz}$
$\\therefore$ Beat frequency, $f_b = f_A' - f_B' = 4\text{ Hz}$