Loading calculator…

What is the Doppler Effect?

The Doppler Effect is a phenomenon where the frequency of a wave received by an observer changes due to the relative motion between the wave source and the observer. We often hear this phenomenon in everyday life: when an ambulance approaches us, its siren sounds higher-pitched (higher frequency), and when the ambulance moves away, its siren sounds lower-pitched (lower frequency). Kalkulab's Doppler Effect Calculator is designed to help high school students, physics students, and acoustics practitioners calculate the observed sound frequency (fp) based on the source velocity (vs), observer velocity (vp), and the speed of sound (v).

Doppler Effect for Sound Waves Formula

fp = fs × (v ± vp) / (v ∓ vs)Formula: If approaching: fp = fs × (v + vp) / (v - vs); If receding: fp = fs × (v - vp) / (v + vs)

Variables:

  • fpObserver Frequency
    Sound frequency heard by the observer(e.g.: 1096.77 Hz)
  • fsSource Frequency
    Sound frequency produced by the source(e.g.: 1000 Hz)
  • vSpeed of Sound
    Speed of sound waves in a given medium, default 340 m/s (air)(e.g.: 340 m/s)
  • vpObserver Velocity
    Observer velocity relative to the medium, positive if approaching the source(e.g.: 20 m/s)
  • vsSource Velocity
    Source velocity relative to the medium, positive if moving away from observer(e.g.: 30 m/s)

Categories:

Stationary Observervp = 0, formula: fp = fs × v / (v ∓ vs)
Stationary Sourcevs = 0, formula: fp = fs × (v ± vp) / v
General CaseBoth moving

How to Use the KalkuLab Doppler Effect Calculator

Follow these steps:

  1. 1

    Select Calculation Mode

    Choose Stationary Observer, Stationary Source, or General (both moving).

  2. 2

    Set Direction of Motion

    Indicate whether source and observer are approaching or receding.

  3. 3

    Enter Frequencies and Speeds

    Enter source frequency (fs), source speed (vs), observer speed (vp), and sound speed (v).

  4. 4

    Click Calculate

    Get observed frequency with full solution steps.

  5. 5

    Analyze Results

    Note whether frequency increased (approaching) or decreased (receding).

💡 Tip:

  • •Use + for approaching motion, − for receding
  • •Sound speed in dry air at 20°C ≈ 343 m/s; often rounded to 340 m/s
  • •Doppler also applies to light (redshift/blueshift) in astronomy
  • •Greater relative speed = larger frequency shift

Examples

Example 1: Approaching Ambulance

Problem:

Ambulance 1000 Hz, 30 m/s toward stationary observer. v=340 m/s.

Solution:
  1. 1.fp = 1000 × 340/(340−30) = 1096.77 Hz
Result:1096.77 Hz

Higher pitch when approaching.

Example 2: Receding Ambulance

Problem:

Same ambulance moving away.

Solution:
  1. 1.fp = 1000 × 340/(340+30) = 918.92 Hz
Result:918.92 Hz

Lower pitch when receding.

Example 3: Observer Moving Toward Siren

Problem:

Stationary 500 Hz siren, observer runs at 5 m/s toward it. v=340.

Solution:
  1. 1.fp = 500 × (340+5)/340 = 507.35 Hz
Result:507.35 Hz

Slight increase because observer approaches the source.

Example 4: Two Cars Approaching

Problem:

800 Hz source at 20 m/s, observer at 15 m/s, both approaching. v=340.

Solution:
  1. 1.fp = 800 × (340+15)/(340−20) = 887.5 Hz
Result:887.5 Hz

Larger shift when both move toward each other.

Example 5: Submarine Sonar in Water

Problem:

10,000 Hz signal, source receding 8 m/s, v=1500 m/s.

Solution:
  1. 1.fp = 10000 × 1500/(1500+8) = 9947 Hz
Result:9947 Hz

Smaller shift in water due to high sound speed.

Frequently Asked Questions

What is the Doppler effect?
Frequency shift when source and observer move relative to each other. Used in astronomy (redshift), weather radar, speed guns, and medical Doppler ultrasound.
When do I use + or − in the formula?
Approaching motion raises observed frequency: + in numerator, − in denominator for source approaching. Receding reverses the signs. Approaching = higher pitch.
Does Doppler apply only to sound?
No—it also applies to light. Redshift (receding) and blueshift (approaching) help measure cosmic velocities.
Why do sirens sound higher when approaching?
Waves compress in front of the source, shortening wavelength and raising frequency (higher pitch).
Same effect in water and air?
Same principle; water's higher sound speed (~1500 m/s) means smaller relative shifts for the same speeds.
Who should use this calculator?
High school and college physics students, acoustics technicians, medical imaging staff, and astronomy learners.
Sound vs light Doppler?
Sound needs a medium; speeds are relative to it. Light in vacuum follows special relativity—relative speed between source and observer matters, no medium required.
Police radar and Doppler?
Radar measures frequency shift of reflected microwaves. Faster vehicles produce larger shifts—this calculator can estimate speed from known frequencies.

Related Calculators

Speed of Sound Calculator

Sound speed in various media

Wave Calculator

Frequency and wavelength

Speed Calculator

Motion analysis

References