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Doppler Effect Simulator

Enter a source frequency, source speed, and observer speed to see how motion changes the perceived pitch. The simulator shows compressed and stretched wavefronts with full step-by-step math.

Wavefront Diagram

Sv_s = 30 m/sOSource: 440 HzObserverf' = 482.2 Hz

Parameters

Hz
m/s
m/s
m/s

Results

Perceived Frequency (f')
482.2 Hz
Frequency Shift
+42.17 Hz
Source Wavelength
0.7795 m
Perceived Wavelength
0.7114 m
Wavelength Change
-0.06818 m
Mach Number
0.0875

Step-by-Step Calculation

1. Doppler Formula (approaching)

f′=f×v+vov−vsf' = f \times \frac{v + v_o}{v - v_s}
f′=440×343+0343−30f' = 440 \times \frac{343 + 0}{343 - 30}
f′=482.2 Hzf' = 482.2 \text{ Hz}

2. Frequency Shift

Δf=f′−f\Delta f = f' - f
Δf=482.2−440\Delta f = 482.2 - 440
Δf=+42.17 Hz\Delta f = +42.17 \text{ Hz}

3. Source Wavelength

λ=vf\lambda = \frac{v}{f}
λ=343440\lambda = \frac{343}{440}
λ=0.7795 m\lambda = 0.7795 \text{ m}

4. Perceived Wavelength

λ′=vf′\lambda' = \frac{v}{f'}
λ′=343482.2\lambda' = \frac{343}{482.2}
λ′=0.7114 m\lambda' = 0.7114 \text{ m}

Reference Guide

The Doppler Formula

When a sound source and observer move relative to each other, the observed frequency changes. The general formula is

f′=f×v±vov∓vsf' = f \times \frac{v \pm v_o}{v \mp v_s}

The upper signs apply when source and observer approach each other, and the lower signs when they move apart.

Approaching vs Receding

When a source approaches, wavefronts compress ahead of it, producing a higher-pitched sound. When it recedes, wavefronts stretch out and the pitch drops.

This is why a passing ambulance siren sounds higher in pitch as it approaches and lower as it drives away.

Mach Number and Sonic Boom

The Mach number is the ratio of the source speed to the speed of sound.

M=vsvM = \frac{v_s}{v}

When M≥1M \geq 1, the source outruns its own wavefronts. All the compressed waves pile up into a shock wave, producing a sonic boom.

Everyday Examples

The Doppler effect is everywhere. Ambulance sirens, train horns, and passing cars all demonstrate the pitch shift. Bats use the Doppler shift of their ultrasonic calls to track flying insects.

In astronomy, the same principle applies to light waves. A galaxy moving away from us has its light shifted toward the red end of the spectrum (redshift).