Skip to main content
Pearson+ LogoPearson+ Logo
All Calculators & ConvertersAll calculators

Doppler Effect Calculator

Calculate the observed frequency (or solve for speed) using the Doppler effect. Includes: temperature → speed of sound, wave-compression visual, % shift + pitch label, a full relativistic light solver (z/β/v/f/λ), and an optional audio demo.

Background

The Doppler effect is the change in observed frequency caused by relative motion. For sound, speeds are relative to the medium. For light, we use a simplified 1D relativistic model. Approaching gives a blueshift (higher frequency). Receding gives a redshift (lower frequency).

Enter values

Tip: Sound uses medium speed (optionally from temperature). Light uses a 1D relativistic model.

Tip: Choose “toward” vs “away” using the chips under vₛ and vₒ.

For sound in air at ~20°C, v ≈ 343 m/s.

We convert internally and keep frequencies in Hz.

Uses v ≈ 331 + 0.6T(°C) (air, classroom approximation). Turn off auto if you want to enter v directly.

Only needed when solving for vₛ, vₒ, or v.

Toward increases frequency. Away decreases frequency.

Toward increases frequency. Away decreases frequency.

Options (sound)

Plays a tone for f and/or f′. If your Hz values are outside audible range, we map them to an audible base while keeping the same ratio.

Chips prefill values and calculate immediately.

Enter any one of: redshift z, β, speed v, f & f′, or λ & λ′. We’ll compute the rest (and warn if values disagree).

Tip: If you enter both, we can solve z/β/v.

You can write in meters, nm, or Å (we’ll parse simple units).

z>0 = redshift (receding), z<0 = blueshift (approaching).

Convention: β>0 receding (redshift), β<0 approaching (blueshift).

Options (light)

Light mode computes shift factor, z, β, v, and optional f′/λ′.

Result

No results yet. Enter values and click Calculate.

How to use this calculator

  • Choose Sound or Light.
  • Sound: pick a mode, enter values, choose toward/away.
  • Light: enter any one of (z, β, v, f & f′, or λ & λ′) and we solve the rest.
  • Click Calculate to get the answer + optional steps/visual/audio.

How this calculator works

  • Sound: f′ = f · (v + sₒ·vₒ) / (v − sₛ·vₛ)
  • Speed of sound (air, approx): v ≈ 331 + 0.6T(°C)
  • Light (1D relativistic): f′/f = √((1 − β)/(1 + β)), and z = λ′/λ − 1 = 1/(f′/f) − 1

Formula & Equation Used

Sound Doppler (1D, medium-based):

f′ = f · (v + sₒ·vₒ) / (v − sₛ·vₛ)

Sign convention used here: “toward” = positive, “away” = negative. (That’s what the direction chips control.)

Speed of sound in air (classroom approximation):

v ≈ 331 + 0.6T(°C)

Light Doppler (1D relativistic):

D = f′/f = √((1 − β)/(1 + β))

β = v/c,   z = λ′/λ − 1 = 1/D − 1

Convention: β>0 receding (redshift), β<0 approaching (blueshift).

Notes & Assumptions

  • Sound mode assumes 1D motion along the line joining source and observer.
  • If |vₛ| approaches v (Mach ~ 1), real shock-wave effects can occur.
  • Light mode uses the standard 1D special-relativity Doppler relation (not transverse Doppler).

Example Problem & Step-by-Step Solution

Example 1 — Find observed frequency (sound)

A siren emits f = 500 Hz. Speed of sound is v = 343 m/s. The source moves toward the observer at vₛ = 30 m/s. The observer is stationary (vₒ = 0). Find f′.

  1. Use f′ = f · (v + vₒ)/(v − vₛ).
  2. f′ = 500 · (343 + 0)/(343 − 30) ≈ 548 Hz

Example 2 — Observer moving toward (sound)

A stationary source emits f = 700 Hz. v = 343 m/s. The observer runs toward the source at vₒ = 10 m/s. Source is stationary (vₛ = 0). Find f′.

  1. f′ = 700 · (343 + 10)/(343 − 0) ≈ 720 Hz

Example 3 — Light redshift (z)

A galaxy emits light at f = 5.00×10¹⁴ Hz with redshift z = 0.20. Find f′.

  1. Use f′ = f/(1+z).
  2. f′ = 5.00×10¹⁴ / 1.20 ≈ 4.17×10¹⁴ Hz

Frequently Asked Questions

Q: Why does “toward” increase frequency?

Approaching squeezes wavefront spacing (shorter wavelength), which raises observed frequency.

Q: What if speeds are close to the speed of sound?

As Mach approaches 1, the denominator can get small and real shock-wave effects occur (sonic boom). We warn you.

Q: Why might light inputs “disagree”?

If you enter multiple inputs (e.g., z and β) that don’t match the same shift factor, we’ll show a consistency warning.

Q: Why doesn’t audio match the exact Hz I entered?

If frequencies are outside the audible range, the demo maps them to an audible base while keeping the same ratio.