Doppler Effect Calculator

Calculate observed frequency using the Doppler Effect formula. Perfect for physics problems involving sound waves, electromagnetic radiation, and relative motion.

**Doppler Effect Formula:** f' = f × (v + v_o) / (v - v_s) Where: • f' = Observed frequency (Hz) • f = Source frequency (Hz) • v = Wave speed in medium (m/s) • v_o = Observer velocity (m/s, + toward source, - away) • v_s = Source velocity (m/s, + toward observer, - away) **Sign Convention:** • Observer moving toward source: v_o > 0 • Observer moving away from source: v_o < 0 • Source moving toward observer: v_s > 0 • Source moving away from observer: v_s < 0 **Special Cases:** • Stationary observer: v_o = 0, so f' = f × v/(v - v_s) • Stationary source: v_s = 0, so f' = f × (v + v_o)/v • Both stationary: f' = f (no Doppler shift)
**Example 1 (Ambulance Approaching):** An ambulance siren at 1000 Hz approaches at 30 m/s (observer stationary). • Source frequency = 1000 Hz • Wave speed = 343 m/s (sound in air) • Observer velocity = 0 m/s • Source velocity = 30 m/s (toward observer) • f' = 1000 × 343 / (343 - 30) = 1096 Hz (higher pitch) **Example 2 (Train Departing):** A train horn at 500 Hz moves away at 25 m/s (observer stationary). • Source frequency = 500 Hz • Wave speed = 343 m/s • Observer velocity = 0 m/s • Source velocity = -25 m/s (away from observer) • f' = 500 × 343 / (343 - (-25)) = 466 Hz (lower pitch) **Example 3 (Both Moving):** Observer runs at 5 m/s toward a 440 Hz source moving at 10 m/s toward observer. • Source frequency = 440 Hz • Wave speed = 343 m/s • Observer velocity = 5 m/s (toward source) • Source velocity = 10 m/s (toward observer) • f' = 440 × (343 + 5) / (343 - 10) = 460 Hz **Example 4 (Red Shift - Astronomy):** Galaxy receding at 0.1c emits light at 500 THz (relativistic). For non-relativistic: f' = 500 × (3×10⁸) / (3×10⁸ + 3×10⁷) ≈ 455 THz (Note: Use relativistic formula for v/c > 0.1)

What is the Doppler Effect?

The Doppler Effect is the change in frequency or wavelength of a wave as observed by someone moving relative to the wave source. Moving closer increases frequency (blue shift), moving away decreases it (red shift).

What is the Doppler Effect formula?

The general formula is f' = f(v ± v_o)/(v ∓ v_s), where f' is observed frequency, f is source frequency, v is wave speed, v_o is observer velocity, and v_s is source velocity. Use + when moving toward, - when moving away.

What is red shift and blue shift?

Blue shift occurs when source and observer approach, increasing observed frequency (light appears bluer). Red shift occurs when they move apart, decreasing frequency (light appears redder). This is crucial in astronomy for measuring cosmic velocities.

How is the Doppler Effect used in radar?

Radar guns emit radio waves that reflect off moving objects. The frequency shift of the reflected wave reveals the object's speed. Police radar, weather radar, and speed cameras all use this principle.

Does the Doppler Effect work for light?

Yes! The relativistic Doppler Effect applies to light. Astronomers use it to measure star and galaxy velocities. Redshift of distant galaxies provides evidence for universe expansion.

What are everyday examples of the Doppler Effect?

Ambulance sirens change pitch as they pass, train horns sound different approaching vs departing, and you can hear the pitch change of race cars as they zoom by. These are all Doppler shifts in sound waves.

How do weather radars use the Doppler Effect?

Doppler radar detects precipitation movement by measuring frequency shifts of reflected microwaves. This reveals wind speeds, rotation in storms, and helps identify tornadoes and severe weather patterns.

What is the difference between source and observer motion?

Mathematically, they're different! Source motion affects the wavelength at emission, while observer motion affects how many wavefronts are encountered. However, at low speeds (v << c), the results are nearly identical.

Can the Doppler Effect be used in medicine?

Yes! Doppler ultrasound measures blood flow velocity by detecting frequency shifts in reflected ultrasound waves. It's used to diagnose circulation problems, check fetal heart rates, and assess blood vessel health.

What happens if both source and observer are moving?

Use the full formula f' = f(v ± v_o)/(v ∓ v_s). The numerator accounts for observer motion, the denominator for source motion. Choose signs based on whether they're approaching (+/−) or receding (−/+).

Is there a Doppler Effect for water waves?

Yes! Any wave phenomenon exhibits Doppler shifting. Water waves, sound waves, light waves, and even matter waves all show frequency changes when there's relative motion between source and observer.

How accurate are Doppler speed measurements?

Very accurate! Modern radar guns are accurate to ±1 mph at typical ranges. The precision depends on signal-to-noise ratio, angle of approach, and calibration. Doppler measurements are legally admissible in traffic enforcement.