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 values: $f' = 100 \times \frac{v}{v - 0.8v} = 100 \times \frac{v}{0.2v} = 100 \times 5 = 500$ Hz.
• The frequency increases because the source moves toward the observer, compressing sound waves.

Why D is correct:

• Matches the Doppler formula, which predicts higher frequency when source approaches observer.

Why the others are wrong:

• A: Ignores Doppler shift, assumes no change.
• B: Applies incorrect formula for receding source.
• C: Miscalculates denominator as $v - 0.5v$, yielding 200 Hz doubled erroneously.

Final answer: D