JAMB Physics 2019 Paper

Concept:The Doppler effect describes how the observed frequency $f'$ changes when the sound source and observer are in relative motion.Explanation:The chasing car is the source, moving at $v_s = 20\text{ m/s}$. The car being chased is the observer, moving at $v_o = 15\text{ m/s}$. Since the source is catching up, it approaches the observer while the observer moves away from the source.Take the speed of sound as $v = 340\text{ m/s}$ and the emitted frequency as $f = 1200\text{ Hz}$.The Doppler formula for this case is:$$f' = f\frac{v - v_o}{v - v_s}$$Substitute the values:$$f' = 1200 \times \frac{340 - 15}{340 - 20}$$Simplify:$$f' = 1200 \times \frac{325}{320} = 1218.75\text{ Hz}$$In kilohertz:$$1218.75\text{ Hz} \approx 1.22\text{ kHz}$$Thus, the apparent frequency heard by the driver being chased is $1.22\text{ kHz}$.Answer:$1.22\text{ kHz}$ (Option A).