The app controls are labelled in Italian: below, each label is given as it appears in the app, followed by its English meaning.

Source and observer at rest

1. Instructions
   • Click here to start the 2D Waves app and select at the top left Sorgente: 1 puntiforme (Source: 1 point source);
   • For a better view of the effect
     • select Stop;
     • drag the source to the centre of the screen with the mouse
2. Remarks

The source is at rest with respect to us as we "observe" the phenomenon; the wavefronts appear evenly spaced.

Moving source and stationary observer

1. Instructions
   • Click here to start the 2D Waves app and select at the top left Effetto Doppler: subsonico (Doppler effect: subsonic);
   • Change the velocità della sorgente (source speed) using the corresponding slider
   • Change the frequenza della sorgente 1 (source 1 frequency) using the corresponding slider;
2. Remarks

With the "default" values of the speed and frequency of the source, the expected thinning out and crowding of the wavefronts can be seen. Changing the two source parameters, the animation looks completely different. Can you tell what happens?

The supersonic bang

1. Instructions
   • Click here to start the 2D Waves app and select at the top left Effetto Doppler: supersonico (Doppler effect: supersonic);
   • Change the velocità della sorgente (source speed) using the corresponding slider
   • Change the frequenza della sorgente 1 (source 1 frequency) using the corresponding slider;
2. Remarks

The envelope of the wavefronts forms a characteristic cone, at whose tip the wavefronts are extremely crowded (not to say superposed). Changing the "default" values of the speed and frequency of the source, the animation changes and the supersonic bang condition is lost. In practice the animation becomes the same as in the previous case.