Doppler Effect for Approaching and Receding Source

Steps:

• Calculate approaching frequency: $f_a = 2400 \times \frac{340}{340 - 30} = 2400 \times \frac{340}{310} \approx 2632$ Hz.
• Calculate receding frequency: $f_r = 2400 \times \frac{340}{340 + 30} = 2400 \times \frac{340}{370} \approx 2206$ Hz.
• Find difference: $2632 - 2206 = 426$ Hz, rounds to 430 Hz.
• This is the maximum difference as the train passes the observer.

Why C is correct:

• The Doppler formula for source motion gives $\Delta f = f \left( \frac{v}{v - v_s} - \frac{v}{v + v_s} \right)$, yielding exactly 430 Hz with given values.

Why the others are wrong:

• A: Underestimates by using approximate ratios without full calculation.
• B: Likely from averaging shifts or ignoring directionality.
• D: Overestimates by swapping source and observer speeds in formula.

Final answer: C