Doppler effect increases frequency for source approaching observer Steps:

• Observed frequency (3.0 Hz) exceeds source frequency (2.0 Hz), indicating boat moves towards man.
• Apply Doppler formula for water waves: $f' = \frac{v_w}{v_w - v}$, where $v_w = 0.75$ m/s.
• Substitute values: $3.0 = \frac{0.75}{0.75 - v}$.
• Solve: $0.75 - v = \frac{0.75}{3.0} = 0.25$, so $v = 0.75 - 0.25 = 0.50$ m/s. Why B is correct:
• Calculated speed 0.50 m/s directly towards man matches the Doppler formula for increased frequency. Why the others are wrong:
• A: Moving away decreases frequency below 2.0 Hz.
• C: Moving away at 0.75 m/s yields $f' = 1.0$ Hz, too low.
• D: Moving towards at 0.75 m/s makes denominator zero, yielding infinite frequency.

Final answer: B