Doppler Effect for Approaching Source

Steps:

• Identify the Doppler formula for a source moving toward a stationary observer: f' = f × (v / (v - v_s)), where f is source frequency, v is wave speed, and v_s is source speed.
• Substitute values: f = 0.20 Hz, v = 20 m/s, v_s = 5.0 m/s.
• Calculate: f' = 0.20 × (20 / (20 - 5)) = 0.20 × (20/15) = 0.20 × 1.333 = 0.267 Hz ≈ 0.27 Hz.
• Round to match choice D.

Why D is correct:

• The formula increases frequency when the source approaches, as the denominator (v - v_s) reduces the effective wavelength per the Doppler law for waves.

Why the others are wrong:

• A: Assumes source receding, using v / (v + v_s), which decreases frequency.
• B: Minor miscalculation of 20/(20+5) ≈ 0.80, times 0.20 Hz.
• C: Incorrectly adds speeds without formula, ignoring wave propagation.

Final answer: D