Doppler Effect for Source Approaching Observer

Steps:

• Observed frequency f' = source frequency f + difference = 440 Hz + 22 Hz = 462 Hz.
• Use Doppler formula: f' = f × (v / (v - v_s)), where v = 340 m/s is speed of sound, v_s is train speed.
• Substitute: 462 = 440 × (340 / (340 - v_s)).
• Solve: 462/440 = 1.05 = 340 / (340 - v_s) → 340 - v_s = 340 / 1.05 ≈ 323.81 → v_s ≈ 340 - 323.81 = 16.19 m/s ≈ 16 m/s.

Why B is correct:

• Calculation using Doppler formula gives v_s ≈ 16 m/s, matching option B.

Why the others are wrong:

• A: 15 m/s yields frequency shift of ≈20.7 Hz, less than 22 Hz.
• C: 17 m/s yields shift of ≈22.3 Hz, more than 22 Hz.
• D: 19 m/s yields shift of ≈24.8 Hz, much more than 22 Hz.

Final answer: B