Doppler — Source Moving
Pitch shifts as source approaches/recedes.
Key Notes
Doppler effect: apparent frequency of a wave changes when SOURCE moves relative to OBSERVER.
Source moving TOWARD stationary observer: apparent f INCREASES (waves compressed in front).
Source moving AWAY from stationary observer: apparent f DECREASES (waves stretched behind).
Formula (source moves, observer stationary): f' = f × v/(v ∓ v_s). Minus when source approaches.
v_s = source speed; v = wave speed (in medium).
Higher harmonics shift more than fundamental (in relative terms).
If v_s ≥ v: produces a sonic boom (cone of compressed waves at Mach angle θ = sin⁻¹(v/v_s)).
Used in: weather radar (raindrop velocity), police radar (car speed), medical Doppler ultrasound (blood flow), astronomy (redshift of galaxies).
Formulas
Source moves, observer at rest
Minus when source approaches (higher f'); plus when receding (lower f').
Speed of source v_s
v_s and v are MAGNITUDES; signs handled by formula.
Approaching limit (v_s → v)
Source catches up with its own waves; shock wave forms.
Sonic boom (Mach cone angle)
v_s > v ⇒ supersonic, cone trailing source.
Important Points
APPROACHING source: f apparent > f source.
RECEDING source: f apparent < f source.
Different formulas for source vs observer motion — combined formula handles both.
If v_s = v: f' → ∞ (sound piles up — sonic boom).
Doppler shift is FREQUENCY change. Wavelength compresses ahead, stretches behind.
Police radar measures Doppler shift of reflected EM waves to determine car speed.
Doppler — Source 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.