Two cars move toward a stationary race-finish detector, emitting sound of frequency 300 Hz. Frequencies detected are 330 Hz and 360 Hz. Their separation at race finish is 100 m; speed of sound 330 m s⁻¹. Find time (s) taken by winning car.
Physics · Mixed Chapter
JEE Main Practice

Question

Two cars move toward a stationary race-finish detector, emitting sound of frequency 300 Hz. Frequencies detected are 330 Hz and 360 Hz. Their separation at race finish is 100 m; speed of sound 330 m s⁻¹. Find time (s) taken by winning car.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — For source moving toward fixed detector, f′ = f c/(c−u), so u = c(1−f/f′). Step 2 — Slower car speed is 330(1−300/330) = 30 m s⁻¹. Faster car speed is 330(1−300/360) = 55 m s⁻¹. Step 3 — Starting together, relative displacement is (55−30)t. Step 4 — Separation at finishing instant is 100 m, so t = 100/25 = 4 s.