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

Formation of standing waves in resonant cavities

1. Instructions
   • Click here to start the 2D Waves app and select Risonanza: cavità risonanti 1 (Resonance: resonant cavities 1)
   • To restart the app click on Cancella onde (clear waves);
   • increase the frequency of the wave (using the Frequenza sorgente 1 (source 1 frequency) slider) and restart the app by clicking on Cancella onde;
   • Set the intensity of the wave (using the slider of the same name, Intensità) to its minimum value and start increasing it gradually: in this way you will better select the cavities that are in resonance.
   • Now try lowering the frequency of the wave and observe that, even with the intensity at its maximum, standing waves do not form
2. Remarks
   • You have to wait a certain time for the standing waves to form: this transient is of course due to the time needed for the waves reflected by the bottom of the cavity to interfere with the incoming waves.
   • Only for certain lengths of the cavity do the reflected waves, interfering with the incoming waves, form nodes at fixed points in space. In these cases the image takes on a "stationary" character and no longer looks like a "travelling wave"
   • At low frequencies (that is, at long wavelengths) the "entrance holes" of the resonant cavities are not even "seen": when the wavelength is much larger than the size of the slit, the perforated grid is seen as a single wall.
3. Other experiments: by selecting Risonanza: cavità risonanti 2 (Resonance: resonant cavities 2) at the top left you can carry out a further experiment in which the resonant cavities are "tubes" open at one end and shorter than in the previous case
4. To find out more visit the pages resonant cavities, standing waves, diffraction.

Acoustic resonances of a room in 2D

1. Instructions
   • Click here to start the 2D Waves app and select Risonanza:stanza (Resonance: room)
   • You can change the position of the sources by dragging the blue "crosshair" of each source with the mouse;
   • You can change the frequency of the sources using the Frequenza sorgenti (source frequency) slider
   • To restart the simulation with the sources in their new position, select the Cancella onde (clear waves) command;
   • We also recommend the 3D view, using the command of the same name;
   • You can change the size of the animation using the Risoluzione (resolution) slider
2. Remarks
   • The very symmetric initial positions of the sources were chosen to highlight simple resonant modes;
   • By changing the initial parameters (position and frequency) you can see how they select the resonant modes;
   • Using the Stop command you can stop the animation and build rooms of different sizes with the mouse (after selecting Cancella pareti (clear walls)).
3. Other experiments: to see other examples of two-dimensional standing waves, select at the top left
   • Risonanza: modi NxN (Resonance: NxN modes)
   • Risonanza: modi NxN combinati (Resonance: combined NxN modes)
   • Risonanza: modi NxN acustici (Resonance: acoustic NxN modes)
4. To find out more: visit the pages standing waves in 2D, resonant cavities, normal modes of a rectangular membrane.

Filtering action of resonant cavities

1. Instructions
   • Click here to start the 2D Waves app and select at the top left Risonanza: filtro passa alto 1 (Resonance: high-pass filter 1)
   • Select Risonanza: filtro passa alto 2 (Resonance: high-pass filter 2)
2. Remarks
   • In going from configuration 1 to configuration 2 the frequency of the wave is lowered by default;
   • The efficiency with which the wave passes through the channel drops drastically, so the channel works as a high-pass filter;
   • At the same time the transmission of the wave through the side waveguides becomes more efficient: in practice they "absorb" the wave, hindering its transmission
3. Other experiments: selecting Risonanza: filtro passa basso 1 and Risonanza: filtro passa basso 2 (Resonance: low-pass filter 1 and 2) at the top left, you can see that this time the filtering acts on the high frequencies. The absorption at high frequencies is due this time to the appearance of transverse modes in the resonant cavities, which hinder the transmission of the wave. Of course the different geometry of the filtering walls plays a decisive role in the appearance of these transverse modes.
4. To find out more: visit the pages filters, standing waves in 2D, resonant cavities, normal modes of a rectangular membrane