🔊 Wave Physics & Relative Motion
Doppler Effect Frequency Shift Calculator
Calculate perceived acoustic frequency ($f'$) for moving sound sources (e.g. emergency sirens, horn passes) or relativistic optical wavelength shift for cosmic astronomical bodies.
🚨 Police Siren Approaching (30 m/s)
🚔 Police Siren Receding (30 m/s)
🚄 Fast Train Horn (50 m/s = 180 km/h)
🏃 Running towards Stationary Source
Source & Observer Motion
Hz
m/s
m/s
m/s (Air at 20°C = 343 m/s)
Perceived Observed Frequency (f')
1,095.85 Hz
Frequency Shift ($\Delta f$)
+9.58%
Compressed Wavelength
0.313 m
Musical Pitch Shift
+1.59 Semitones
💡 Acoustic Perception:
As the source approaches at 108 km/h (30 m/s), wave fronts are compressed in front of the vehicle, raising perceived pitch by ~1.6 musical semitones.
The Acoustic Doppler Formula
Christian Doppler formulated the frequency shift caused by relative motion between emitter and observer:
$$f' = f_0 \left(\frac{v \pm v_o}{v \mp v_s}\right)$$
- Sign Convention: Top signs ($+ v_o, - v_s$) apply when moving towards one another; bottom signs ($- v_o, + v_s$) apply when moving away.
- Mach Limit: If source velocity $v_s \ge v$, a supersonic shockwave (sonic boom) forms, and the linear acoustic formula is superseded by conical shock dynamics.