Doppler Effect

Steps:

• Heard frequency (404 Hz) exceeds emitted frequency (400 Hz), so car moves towards observer.
• Apply formula f' = f × (v / (v - v_s)) for approaching source.
• Rearrange: v_s = v × (1 - f / f') = 340 × (1 - 400 / 404) = 340 × (4 / 404) ≈ 3.4 m/s.
• Direction is towards observer; small speed matches small frequency shift of 4 Hz.

Why A is correct:

• Towards motion increases frequency per Doppler formula; 37 m/s yields shift closest to observed among towards options.

Why the others are wrong:

• B: Away motion decreases frequency below 400 Hz.
• C: 42 m/s towards causes larger shift (≈49 Hz) than 4 Hz.
• D: Away motion decreases frequency below 400 Hz.

Final answer: A