Doppler Effect for Approaching Source

Steps:

• Identify the Doppler formula for a source approaching a stationary observer: $f' = f \times \frac{v}{v - v_s}$, where $f = 100$ Hz, $v_s = 0.8v$, and $v$ is the speed of sound.
• Substitute $v_s = 0.8v$ into the denominator: $v - v_s = v - 0.8v = 0.2v$.
• Compute the ratio: $\frac{v}{0.2v} = 5$.
• Multiply: $f' = 100 \times 5 = 500$ Hz.

Why D is correct:

• The formula directly yields 500 Hz, as the approaching source compresses wavefronts, increasing observed frequency by the factor $\frac{v}{v - v_s} = 5$.

Why the others are wrong:

• A: 56 Hz ignores the approach, mistakenly applying recession formula.
• B: 180 Hz misapplies relativistic Doppler for light, not sound.
• C: 400 Hz uses incorrect factor like $\frac{v}{v - 0.75v}$, not 0.8v.

Final answer: D