Doppler effect

A sound source is moving with velocity v along the horizontal axis. Every period T a wave front leaves the source and travels with velocity c with respect to a medium (say air), which may be still or move with velocity (V_x, V_y) = (Vx, Vy). A detector is located at position (x, y) and may move with velocity (dx/dt, dy/dt).

You may edit the values of the aforementioned quantities, as well as the time interval dt between animation frames.
The detector position may also be chosen by means of the mouse.
Press Initial to set t = 0 and the source at its initial position.
Press Continue to start or continue the animation.
Press Stop to pause the animation, and Reset to recover the default settings.

In the graphics window below the animation a vertical red (green) bar is displayed each time a wave front leaves the source (reaches the detector).

Activities

With the default values you may see (in the animation and in the graphics) the Doppler effect at work: when source and detector are approaching (moving away) the time interval is shorter (larger) between detections than between emissions, i.e., the detected frequency is higher (lower).
Click over the bars corresponding to consecutive emissions (detections) to see the corresponding times. Use the latter to check that the periods agree with the theoretical result for the detected period:
T' = (1-v/c) T and T' = (1+v/c) T.
Repeat the previous check when the detector moves with a positive (negative) horizontal velocity dx/dt.
Repeat the previous checks when the medium moves with a positive (negative) horizontal velocity V_x.
(You may also be curious about what happens when dy/dt and/or V_y are non zero.)
Use the mouse to put the detector out of the source trajectory, press Initial and then Continue. You should observe that when the wave front reaches the source in a direction perpendicular to the source motion the transverse Doppler effect is nil (but not in special relativity: recall the Ives-Stilwell experiment).
Check that in the supersonic case (v ≥ c) a shock wave develops. Press Stop and click the mouse at different points of the shock to check the theoretical angle.

This is an English translation of the Basque original for a course on mechanics, oscillations and waves.
It requires Java 1.5 or newer and was created by Juan M. Aguirregabiria with Easy Java Simulations (Ejs) by Francisco Esquembre. I thank Wolfgang Christian and Francisco Esquembre for their help.