Doppler Effect Calculator
Solve f_obs = f_source × v_sound / (v_sound ∓ v_source) for the frequency heard when a sound source moves toward or away from a stationary listener. Two 3D diagrams show compressed wavefronts ahead of the source and stretched wavefronts behind it, and charts compare observed frequency across a range of source speeds.
Reviewed by the ToolNestr Editorial Team — July 2026
Compressed vs stretched wavefronts
1. Ahead of the source — compressed
Wavefronts bunch closely together on the approaching side, since each new wave is emitted from a position closer to this side than the last — a higher observed frequency.
2. Behind the source — stretched
Wavefronts spread farther apart on the receding side, since each new wave is emitted from a position farther from this side — a lower observed frequency.
Doppler shift graphs
How it works
The core idea in one line: A moving sound source compresses the wavefronts ahead of it and stretches them behind it, so a stationary listener hears a higher pitch as the source approaches and a lower pitch as it recedes — even though the source's true emitted frequency never changes.
fobs = fsource × vsound / (vsound − vsource)
source approaching the observer (pitch rises)
fobs = fsource × vsound / (vsound + vsource)
source receding from the observer (pitch falls)
For an approaching source, f_obs = f_source·v_sound/(v_sound − v_source) — the minus sign in the denominator makes f_obs larger than f_source. For a receding source, f_obs = f_source·v_sound/(v_sound + v_source) — the plus sign makes f_obs smaller. Both formulas reduce to f_obs = f_source when v_source = 0, and the approaching case grows without bound as the source speed approaches the speed of sound itself.
Worked example 1 — approaching siren
Given: A siren emits f_source = 700 Hz. It approaches a stationary listener at v_source = 30 m/s, with v_sound = 343 m/s. Find the observed frequency.
The approaching source compresses the wavefronts, so the listener hears a higher pitch than the 700 Hz actually emitted.
Worked example 2 — receding siren
Given: The same siren (f_source = 700 Hz, v_sound = 343 m/s) now recedes from the listener at v_source = 30 m/s. Find the observed frequency.
Receding stretches the wavefronts, lowering the observed pitch below the true 700 Hz — this is the drop in pitch heard just after a siren passes by.
Approaching vs receding — same speed, opposite effect
At the same source speed, approaching raises frequency more than receding lowers it, because the formulas are not symmetric around the source frequency.
| Source speed | Approaching f_obs | Receding f_obs |
|---|---|---|
| 0 m/s | 700.00 Hz | 700.00 Hz |
| 30 m/s | 767.09 Hz | 643.70 Hz |
| 60 m/s | 848.94 Hz | 598.76 Hz |
| 100 m/s | 1000.00 Hz | 564.63 Hz |
f_source = 700 Hz, v_sound = 343 m/s in all rows. The approaching case grows without bound as v_source approaches v_sound, while the receding case only asymptotically approaches zero.
Where the Doppler effect actually matters
🚑 Emergency vehicle sirens
The pitch shift of an approaching-then-receding ambulance or fire truck siren is a direct, everyday demonstration of the Doppler effect, and drivers instinctively use the changing pitch to judge whether a vehicle is approaching or moving away.
🚔 Police radar and speed guns
Radar guns bounce a radio wave off a moving vehicle and measure the Doppler shift in the reflected frequency to calculate the vehicle's speed — the same v = fλ and Doppler relationships used for sound apply to these electromagnetic waves.
🌌 Astronomical redshift
Light from galaxies moving away from Earth is Doppler-shifted to longer (redder) wavelengths, and this redshift is one of the primary pieces of evidence for the expansion of the universe.
🌦️ Doppler weather radar
Weather radar stations measure the Doppler shift of radio waves reflecting off raindrops or debris to determine wind speed and direction inside storms, which is essential for detecting tornadoes and severe weather rotation.
Common misconceptions
"The Doppler effect changes the actual frequency the source emits."
The source's emitted frequency never changes — only the frequency an outside observer perceives changes, because of how the wavefronts get compressed or stretched by the source's motion relative to the observer.
"Approaching and receding shift the frequency by the same amount, just in opposite directions."
The two formulas aren't symmetric: f_obs = f_source·v/(v−v_source) for approaching grows without bound as v_source nears v, while f_obs = f_source·v/(v+v_source) for receding only approaches zero — the size of the shift differs between the two cases at the same speed.
"The Doppler effect only happens when the source is moving, not the observer."
The effect happens for either the source or the observer moving (or both) — a moving observer toward a stationary source also hears a higher frequency, though the exact formula differs slightly from the moving-source case used here.
"You need to be moving toward or away in a straight line for the Doppler effect to apply."
The Doppler shift depends on the component of relative velocity along the line connecting source and observer — an object moving past you at an angle produces a smaller, continuously changing shift, not zero shift, except at the instant it is moving directly perpendicular to your line of sight.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 1 — §17.4 "The Doppler Effect" (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 17, Waves II (The Doppler Effect).
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 17, Sound Waves.
f_obs = f_source × v_sound / (v_sound ∓ v_source), for a moving source and stationary observer, with v_sound ≈ 343 m/s in air at room temperature. Results are rounded for display.
How to use this calculator
Enter the source frequency
This is the true frequency emitted by the moving source, in hertz.
Set speed of sound and source speed
v_sound defaults to 343 m/s for air; adjust for other temperatures or media if needed.
Toggle direction
Switch between approaching (higher observed pitch) and receding (lower observed pitch).
Related tools
Frequently asked questions
What is the Doppler effect?
The Doppler effect is the change in observed frequency of a wave caused by relative motion between the source and the observer. A sound source moving toward you raises the pitch you hear (higher frequency); a source moving away lowers it (lower frequency), even though the source itself never changes its actual emitted frequency.
What is the formula for a moving source and stationary observer?
f_obs = f_source × v_sound / (v_sound − v_source) when the source approaches, and f_obs = f_source × v_sound / (v_sound + v_source) when it recedes, where v_sound ≈ 343 m/s in air at room temperature. The minus sign in the denominator raises the observed frequency; the plus sign lowers it.
Why does a passing ambulance siren change pitch?
As the ambulance approaches, each successive sound wave is emitted from a position slightly closer to you than the last, compressing the wavefronts and raising the frequency you hear. Once it passes and recedes, each wave is emitted farther away, stretching the wavefronts and lowering the pitch — the classic 'eee-yoooown' effect.
Does the Doppler effect only apply to sound?
No — it applies to any wave phenomenon, including light. The same underlying principle causes the redshift and blueshift of light from stars and galaxies moving away from or toward Earth, which astronomers use to measure cosmic expansion and the motion of distant objects.
What happens if the source moves faster than the speed of sound?
If v_source ≥ v_sound, the source is moving faster than the waves it emits can travel forward, and the standard formula breaks down (the denominator would be zero or negative for the approaching case). This is the regime of sonic booms, where wavefronts pile up into a shock cone instead of separate compressed waves.