Doppler Effect for Moving Source

Steps:

• Use Doppler formula for source moving away: $f' = f \frac{v}{v + v_s}$, where $f' = 20$ Hz, $f = 30$ Hz, $v = 330$ m/s.
• Set up equation: $20 = 30 \frac{330}{330 + v_s}$.
• Simplify: $\frac{20}{30} = \frac{330}{330 + v_s}$, so .
• Solve: $330 + v_s = 330 \times \frac{3}{2} = 495$, thus m/s away.

Why C is correct:

• Matches Doppler formula for receding source, where lower observed frequency indicates motion away at calculated speed.

Why the others are wrong:

• A: Wrong speed; 110 m/s yields $f' \approx 23.1$ Hz, not 20 Hz.
• B: Wrong direction and speed; towards would increase frequency above 30 Hz.
• D: Wrong direction; towards at 165 m/s yields $f' \approx 60$ Hz.

Final answer: C