• word_count: 200

Common Doppler scenarios in JEE: (1) Reflection from a wall: A source at speed $v_s$ toward a wall produces a reflected frequency $f_r = fv/(v-v_s)$ (wall receives and re-emits). A stationary observer between source and wall hears beats at $\approx 2fv_s/v$ (for $v_s \ll v$). (2) Two vehicles approaching: Both approaching gives maximum shift: $f' = f(v+v_o)/(v-v_s)$. (3) Source passing observer: Frequency drops from $fv/(v-v_s)$ to $fv/(v+v_s)$ as the source passes. The ratio of these frequencies can be used to find $v_s$ without knowing $f$.

Important special cases: (a) Source and observer moving together at the same speed — no Doppler shift ($f' = f$). (b) Source perpendicular to the line of observation — no classical Doppler shift. (c) Wind blowing — replace $v$ with $v \pm v_w$ in both numerator and denominator; for stationary source and observer, wind alone produces no shift.

Always convert km/h to m/s ($\times 5/18$) before applying the formula. Sanity check: approaching should increase frequency; receding should decrease it. If your calculated $f'$ violates this, recheck signs.