Doppler Effect for Moving Source Steps: - The observed frequency is lower than the source frequency (450 Hz < 500 Hz), indicating the train is moving away from the person. - Use the Doppler formula for source moving away: $f' = f \frac{v}{v + v_s}$, where $f' = 450$ Hz, $f = 500$ Hz, $v = 340$ m/s. - Substitute: $450 = 500 \frac{340}{340 + v_s}$; simplify to $0.9 = \frac{340}{340 + v_s}$. - Solve: $340 + v_s = \frac{340}{0.9} \approx 377.78$; $v_s \approx 37.78$ m/s, or 38 m/s. Why C is correct: - The formula $f' = f \frac{v}{v + v_s}$ for receding source yields exactly 38 m/s, matching the decreased frequency per Doppler principle. Why the others are wrong: - A: 34 m/s is the incorrect calculation without the full Doppler adjustment (ignores the 0.9 factor). - B: Towards the person would increase frequency above 500 Hz, not decrease it. - D: 38 m/s towards would raise frequency to about …