The Doppler effect

Equipment

• Moving sound source emitting circular wavefronts on a 3D surface
• “Emitted frequency f” slider
• “Source speed / sound speed” slider
• “Time step between wavefronts” slider, “Pause” button and the f′ readout line

Procedure

1. Freeze and measure the wavefront spacing on both sides

   Press “Pause” after the source has emitted several wavefronts: ahead of the source the circles bunch (short wavelength, high frequency), behind they spread (long wavelength, low frequency). Drag to rotate for a clear view of the compressed and stretched regions.

2. Vary the source speed and check the Doppler formula

   Raise “Source speed / sound speed”: as $v_s$ approaches $v$, the fronts ahead compress more. Read the formula line below the figure and check that $f' = fv/(v - v_s)$ diverges as $v_s \to v$ — the precursor of a shock wave.

3. Change the emitted frequency and the time step

   Raise “Emitted frequency f” while keeping the source speed fixed: the wavelength shrinks but the relative front/back compression stays the same, since the ratio $f'/f = v/(v \mp v_s)$ does not depend on f. Adjust “Time step between wavefronts” to thin or densify the rings for easier reading.

Simulation

Experiment history

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