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

Changing the intensity of a wave

1. Instructions
   • Click here to start the app and in the "Forme d'onda" (waveforms) window select Seno (sine)
   • Select Suono (sound) with the mouse;
   • Change the Volume with the corresponding slider.
2. Remarks
   • You will have heard that the sound (of course) becomes more or less loud (which is exactly what we mean in everyday language).
   • You will have noticed that the waveform changes its amplitude. You can deduce that the loudness of the sound (volume) is closely related to the amplitude of the wave.
3. Related topics: the sound wave, perception of loudness

Changing the frequency of a wave

1. Instructions
   • Click here to start the app and in the "Forme d'onda" (waveforms) window select Seno (sine)
   • Select Suono (sound) with the mouse;
   • Change the Frequenza della fondamentale (frequency of the fundamental) with the corresponding slider.
2. Remarks
   • You will have heard that the sound becomes higher or lower (musicians would say the "note" changes); you can therefore deduce that the perceived pitch is closely related to the frequency.
   • Related topics: the sound wave, perception of pitch

Relation between loudness and pitch (frequency glissando)

1. Instructions
   • Click here to start the app and in the "Forme d'onda" (waveforms) window select Seno (sine)
   • Select Suono (sound) with the mouse;
   • Set the volume to an intermediate level (NOTE: it may work better to set the volume to the maximum and change the volume with the control on your headphones or your PC.)
   • Keeping the volume constant, use the corresponding slider to change the frequenza della fondamentale (frequency of the fundamental) from the minimum to the maximum possible value.
   • With the frequency at its minimum value, increase the volume so that the sound becomes audible
2. Remarks
   • As the sound becomes lower, the perceived loudness decreases until it disappears, while as the sound becomes higher, the perceived loudness increases up to the limit of tolerance.
   • Note that during the process the amplitude of the wave, which in the first experiment seemed to be the factor determining loudness, stays the same.
   • Amplitude, although decisive, is not the only factor determining perceived loudness.
3. To find out more: visit the page perception of loudness, which explains the concept of the equal-loudness contour that accounts for the dependence of perceived loudness on the frequency of the sound.

Relation between loudness and pitch (amplitude glissando)

1. Instructions
   • Click here to start the app and in the "Forme d'onda" (waveforms) window select Seno (sine)
   • Select Suono (sound) with the mouse;
   • Try setting the volume to a comfortable level (NOTE: it may work better to set the volume to the maximum and change the volume with the control on your headphones or your PC.)
   • Start changing the volume with the corresponding slider and listen carefully to the pitch of the sound.
2. Remarks
   • When the sound becomes louder it also seems to become slightly lower (that is, its pitch seems to drop), while when the sound becomes softer it also seems to become slightly higher (that is, its pitch seems to rise).
   • The frequency of the wave has not changed, yet a change in perceived pitch is observed, induced by the change in loudness of the sound.
   • The experiment shows a correlation between loudness and pitch: the frequency of the sound, although it is the decisive factor in producing the sensation of pitch (as shown in the previous experiment), is not the only one.
   • This has important consequences for musicians and listeners: listening to a tenor from the front row, where the sound is very loud, or to an orchestral passage going from pianissimo to fortissimo, can cause significant shifts in the perceived frequency, with the sensation of a flat note (lower than the correct intonation).
3. Related topics: the sound wave, perception of pitch and perception of loudness.

Beats

1. Instructions
   • Click here to start the app and in the "Trasformazioni" (transformations) window select "Cancella tutto" (clear all)
   • Using the corresponding slider, lower the Frequenza della fondamentale (frequency of the fundamental) to its minimum value (9 Hz)
   • Using the amplitude palette, raise to the maximum the amplitude of two consecutive harmonics (in this way you will superpose two harmonics whose frequencies differ by exactly the frequency of the fundamental). Choose harmonics in the region around 200 Hz, so that the beat condition is met, that is, the difference between the two frequencies involved is much smaller than the individual frequencies.
   • If you want to hear the sound of the beats, activate "suono" (sound) in the corresponding window.
2. Remarks
   • The waveform resulting from the superposition of two waves that meet the beat condition shows the classic "double periodicity": the signal is amplitude-"modulated" at a frequency equal to the beat frequency.
   • As far as sound is concerned, the amplitude modulation produces a variation in the perceived loudness; given the low beat frequency chosen, the sound becomes intermittent.
3. Other experiments
   • Leaving "suono" (sound) active, try gradually increasing the "Frequenza della fondamentale" (frequency of the fundamental). The intermittent character becomes less perceptible: the sound resembles that of cooing "doves" and is unpleasant to listen to ("dissonant").
   • Try moving gradually away from the beat condition: by increasing the frequency of the fundamental and choosing lower harmonics (e.g. the second and third), the double periodicity of the waveform becomes less evident. As far as sound is concerned, the sound becomes pleasant ("consonant"): the two sounds are not perceived as distinct.
   • Repeat the previous experiment as follows:
     • listen for a while, separately, to the two harmonics to be superposed, so as to accustom your ear to the perception of their frequency;
     • now start superposing the third harmonic on the second: by adding a higher-frequency wave you would expect to get a "higher" sound; surprisingly, you will hear the sound drop (become lower), as if the fundamental frequency, although not invited, had joined the superposition of its harmonics. This is the perceptual phenomenon of virtual pitch. If you want to explore the question further, visit the page perception of pitch.
     • If you want to check that the low sound you perceive really has the frequency of the fundamental, actually add it using the "palette" for its amplitude.
4. Related topics: perception of pitch, physiology of the auditory system and critical bands