Engineering
Doppler Effect frequency shift & compressed sound wavelength formula
Calculate observed acoustic frequency f_obs = f_src * (c + v_obs) / (c - v_src) and wavefront wavelength for approaching vs. receding sound sources.
Keep observer vs. source sign conventions straight in the Doppler equation!
For sound waves traveling through air at speed c (~340 m/s), relative motion shifts the pitch heard by an observer via f_obs = f_src * (c + v_obs) / (c - v_src), where v_obs is positive when the observer moves TOWARD the source and v_src is positive when the source moves TOWARD the observer (negative when receding!).
Notice the physical asymmetry: an ambulance emitting 680 Hz while approaching a stationary listener at v_src = +34 m/s (0.10 Mach) compresses wavefronts ahead of it to lambda = (340 - 34) / 680 = 0.45 m, raising observed pitch to 680 * 340 / 306 = 755.56 Hz; once it passes (v_src = -34 m/s), pitch drops to 680 * 340 / 374 = 618.18 Hz!
This classical acoustic model assumes motion along the propagation line in a stationary, uniform medium, with source and observer speeds measured relative to that medium. The example restricts both speed magnitudes below sound speed. It does not cover sonic shocks, arbitrary transverse geometry, wind gradients or light-wave relativity.
| Doppler Scenario (f_src = 680 Hz, c = 340 m/s) | Formula | Observed Result |
|---|---|---|
| Approaching Siren (v_src = +34 m/s, v_obs = 0) | 680 * (340 + 0) / (340 - 34) | 755.56 Hz (+75.56 Hz shift) |
| Receding Siren (v_src = -34 m/s, v_obs = 0) | 680 * (340 + 0) / (340 - (-34)) | 618.18 Hz (-61.82 Hz shift) |
| Compressed Forward Wavelength (m) | (340 - 34) / 680 | 0.45 m (vs. 0.50 m at rest) |
Observed Doppler-shifted frequency (Hz)
A2=SourceFreq_Hz (680), B2=SoundSpeed_m_s (340), C2=ObserverTowardSpeed (0), D2=SourceTowardSpeed (+34 approaching, -34 receding).
=IF(OR(COUNT(A2:D2)<>4,A2<=0,B2<=0,ABS(C2)>=B2,ABS(D2)>=B2),"Invalid inputs",ROUND(A2 * (B2 + C2) / (B2 - D2), 2))Wavelength in the medium along the source-to-observer direction
The medium wavelength is (c-v_source)/source frequency. Observer motion changes the arrival frequency but does not itself change this medium wavelength. Positive source speed here points toward the observer; negative is receding.
=IF(OR(COUNT(A2:D2)<>4,A2<=0,B2<=0,ABS(C2)>=B2,ABS(D2)>=B2),"Invalid inputs",ROUND((B2 - D2) / A2, 3))Try the example
Use the original values or change them to test your understanding.