Doppler effect calculator (sound)
f′ = f · (v + v_obs) / (v − v_src)
The siren that rises then “drops” as it passes, computed properly: f′ = f·(v + v_obs)/(v − v_src), with one sign convention displayed everywhere (positive = approaching) that covers all four cases without juggling ±. The tool shows the real asymmetry between a moving source and a moving observer (at 30 m/s, 482 Hz versus 478 Hz on an A440) and names the impossibilities: source at the sound barrier (Mach cone), observer outrunning the sound.
482.17 Hz
- Calculation
- f′ = f·(v + v_obs)/(v − v_src) = 440 × (343 + 0) ÷ (343 − 30) = 482.17 Hz
HIGHER pitch: 482.17 Hz, that is +42.173 Hz. Approaching compresses the waves (or crosses them faster).
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasf′ = f · (v + v_obs) / (v − v_src)
f′ = f · (v + v_obs) / (v − v_src)
convention: positive speed = approaching, negative = receding
wavelengths: λ′ = v / f′
Two distinct mechanisms hide in one formula: an approaching source compresses the waves in the medium (the denominator shrinks), while an approaching observer crosses unchanged waves more often (the numerator grows). That is why source and observer are not interchangeable: at 30 m/s toward the other, a moving source gives 482.2 Hz where a moving observer gives 478.5 Hz, on the same A440. The asymmetry vanishes at low speeds, where both tend to f·(1 + u/v).
- The sign convention
- · the single real difficulty of the topic. Here: positive = approaching, negative = receding. For both actors. Any other convention works too, provided you never switch mid-calculation.
- Speed of sound (v)
- · ≈ 343 m/s in air at 20 °C; it grows by about 0.6 m/s per degree and changes with the medium (water ≈ 1,480 m/s). The speeds in the formula are measured relative to the MEDIUM, not between the actors.
- Sound barrier
- · when the source reaches v, the forward-emitted waves pile up on it, the Mach cone and the sonic boom. The Doppler formula diverges exactly there: its domain stops at the barrier.
Validity domainOne-dimensional acoustic model: motions are assumed along the source-observer line (for a pass at a distance, only the radial component counts, and it varies continuously).
One-dimensional acoustic model: motions are assumed along the source-observer line (for a pass at a distance, only the radial component counts, and it varies continuously). The medium is assumed still, a constant wind is handled by adding its speed to both actors. The luminous (relativistic) Doppler effect follows a different, medium-free. Symmetric formula. Outside this tool.
Common pitfall: the siren does not “rise” while approachingAt constant speed, the perceived frequency is constant during the whole approach (higher than f), then constant during the whole recession (lower): the famous “drop” happens only at the moment of passing.
At constant speed, the perceived frequency is constant during the whole approach (higher than f), then constant during the whole recession (lower): the famous “drop” happens only at the moment of passing. The impression that the sound rises while approaching comes from the growing loudness, not the pitch. Another trap: using the relative speed between source and observer, sound propagates in a medium. And speeds count relative to it; that is what makes source and observer non-interchangeable.