Doppler Effect 2D – AP Physics 1

Doppler Equation

$$ f' = f \left( \frac{v \pm v_o}{v \mp v_s} \right) $$

The frequency $f'$ perceived by an observer changes if the source ($v_s$) or the observer ($v_o$) is moving relative to the medium.

Key Regimes

Subsonic ($M < 1$): Waves compress ahead (higher pitch, blue shift) and stretch behind (lower pitch, red shift).

Transonic ($M = 1$): Source matches the speed of sound. Wavefronts stack into a sound barrier.

Supersonic ($M > 1$): Source outruns the waves, creating a Mach Cone (Sonic Boom) trailing behind.

Tags

acousticswavesfrequencymach

Wave Analytics

Source Speed (Mach) 0.5

Emission Frequency (Hz) 4.0 Hz

Observer locations are assumed infinitely far directly ahead and directly behind the source along the X-axis for frequency calculations.