Doppler Effect Simulator

A moving source can't outrun its own waves — but it can chase them. Each new wavefront is emitted from a point closer to an observer ahead, so the crests arrive bunched together: higher pitch. Behind, they stretch apart: lower pitch. Drive the source in this simulator and watch the wavefront spacing — and the observed frequency — respond.

Source speed 60 px/s

Emitted 1.0 HzWave speed 140 px/sf′ = f / (1 ∓ vₛ/v)

Controls

Source speed: How fast the wave source moves in m/s. Positive values approach the observer; negative values recede.
Wave frequency: The frequency the source actually emits in Hz — the wavefronts per second leaving the source.

The physics

f' = f\frac{v}{v - v_s}

Observed frequency — source approaching

f' = f\frac{v}{v + v_s}

Observed frequency — source receding

\lambda' = \lambda \mp \frac{v_s}{f}

The wavelength itself is squeezed or stretched by the source's motion

Assumptions

Source speed is below the wave speed (no shock wave)
The observer is stationary
The medium is uniform — wave speed v is constant
One-dimensional motion along the line to the observer

Guided activity

Set source speed to 0 m/s. The wavefronts are evenly spaced and the observed frequency equals the emitted one — the baseline.
Set source speed to 30 m/s toward the observer (f = 700 Hz, v = 343 m/s). Compute the observed frequency with the formula and compare with the readout.
Flip the source to recede at 30 m/s. By what fraction does the observed frequency drop? Why isn't the shift symmetric with the approaching case?
Raise the source speed toward 300 m/s. What happens to the wavefronts ahead of the source? What would occur at v_s = v?

Challenge questions

As v_s approaches v, the approaching formula's denominator shrinks toward zero. Explain in terms of wavefronts why the observed frequency skyrockets — and what a sonic boom is.
An ambulance passes you: the pitch drops suddenly at the moment it passes, not gradually. Why is the change abrupt rather than smooth?
The same math describes redshift of distant galaxies. If light from a galaxy is redshifted, is the galaxy approaching or receding — and what does the size of the shift tell us?