A source of sound $S$ of frequency $500\text{ Hz}$ situated between a stationary observer $O$ and moves…
A source of sound $S$ of frequency $500\text{ Hz}$ situated between a stationary observer $O$ and moves towards the wall with a speed of $2\text{ ms}^{-1}$. If the velocity of sound is $332\text{ ms}^{-1}$, then the number of beats per second heard by the observer is (approximately)
8
6
4
2
Solution
For direct sound, source is moving away from the observer so frequency heard in this case,
[Diagram showing observer O, source S moving right away from O with speed $v_s$ towards a wall, and image source S'.]
$f_1 = f \left( \frac{v}{v + v_S} \right) = 500 \left( \frac{332}{332 + 2} \right) = 500 \left( \frac{332}{334} \right)\text{ Hz} \approx 497\text{ Hz}$
For sound reflected from the wall,
$f_2 = f \left( \frac{v}{v - v_s} \right) = 500 \left( \frac{332}{332 - 2} \right) \approx 503\text{ Hz}$
$\therefore$ Beat frequency $= f_2 - f_1 = 6\text{ Hz}$