Doppler — Both Moving
f' = f(v±v_o)/(v∓v_s).
Key Notes
When BOTH source and observer move, use the COMBINED Doppler formula.
f' = f·(v ± v_o)/(v ∓ v_s). Top sign: observer approaches source. Bottom sign: source approaches observer.
Approach geometry: + in top, − in bottom ⇒ shift UP.
Receding geometry: − in top, + in bottom ⇒ shift DOWN.
Sign convention is the trickiest part — drawing a diagram helps.
Special case: if source and observer move at same velocity, f' = f (no relative motion).
Applications: aircraft tracking radar (both moving), astronomy (both rotating), military sonar (both ships moving).
Relativistic effects matter when speeds approach c — modified formulas for light.
Formulas
Combined Doppler
Top sign: observer; bottom sign: source. Approach ⇒ + on top, − on bottom.
Both approaching
Highest possible f' if both motions add constructively.
Both receding
Lowest possible f' (both subtract from waves received per second).
Same velocity (no relative motion)
v_s = v_o, both moving same direction ⇒ no shift.
Important Points
Sign convention is CRUCIAL — draw a picture, label motion directions, decide if each motion ADDS or SUBTRACTS from received frequency.
Both approaching = MAX f shift up.
Both receding = MAX f shift down.
Common pitfall: using observer formula for moving source (or vice versa).
Light/EM Doppler: combined-motion formula differs (relativistic factors).
Real-world: radar uses combined Doppler to track both moving plane and moving radar dish.
Doppler — Both Moving notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.