From "Physics, Waves, Music": a website about the physics of waves and sound, acoustics of musical instruments, musical scales, harmony and music.
Vibrations, supersonic bangs and sources of impulsive noise
In this video, various sources of both impulsive noise and noise generated by vibration and resonance are illustrated through comments on high-speed videos. These allow us to see phenomena that our eyes cannot resolve but that our ears can. See the page on Sound and resonance as well.
In the following paragraphs, we have created several acoustic examples to put the traditional distinction between sound and noise to the test.
Three easy "pieces"
Many elementary surveys on this topic affirm that what seems to characterise sound with respect to noise is its description in terms of a periodic wave. The spectrum must contain only pure sounds (sinusoidal components) whose frequencies are multiples of a fundamental frequency.
The following are graphic illustrations of waves that are periodic and non-periodic with their respective spectrograms and corresponding sound (click on the images to enlarge them and on the audio files to listen to them. If you want more information on how to read a spectrogram, visit this page with instructions)
Graph
Spectrogram
Audio
puro_220_Hz.wav
Pure (sinusoid) sound at 220 Hz.
triangolo_220_Hz.wav
Triangular wave with fundamental at 220 Hz.
rumore_bianco.wav
White noise (uniform spectrum).
Let us first observe that not all sounds associated with a periodic wave are "pleasant" (many listeners find sinusoid and triangular waves irritating and, certainly, beyond any subjective judgement of pleasantness, they are "objectively" uninteresting. However, if we limit ourselves to these examples, it seems to confirm the most elementary association: a well-defined pitch can be associated with a periodic wave, while it cannot be attributed to white noise. For example, it does not make sense to ask ourselves if it is higher or lower than the sinusoid. To put the definition to the test, we should consider a few, more complex examples.
Less easy "Pieces"
This question is a bit more complex. Wave periodicity is not a sufficient condition to call what we hear sound, even if we neglect the aesthetic judgement of the sounds produced by periodic signals. In fact we cannot say that periodic waves necessarily generate sounds within the range of audible frequencies. Listen to the AUDIO example below.
Graph
Spectrogram
Audio
battimenti_220_245_Hz.mp3
Overlapping of two pure sounds at 220 and 245 Hz
Even with the presence of a periodic wave (the graph leaves no doubt), it would be difficult to call what you just heard sound. You just listened to what is called in acoustics a beat. In this case, the sensation of noise (even with the presence of periodic waves) is due to a perceptual mechanism: our auditory system is "confused" when it is hit by sounds of very close frequencies and is unable to discriminate their pitch, it perceives a sound with an intermediate pitch but of a "rough" nature, therefore, noisy.
This is how the two components sound when heard individually (if you wish to study this topic further, visit the page on critical bands and beats).
puro_220_Hz.mp3
Pure sound at 220 Hz
puro_245_Hz.mp3
Pure sound at 245 Hz
"Harmonic noise"
It is easy to realise that (exact) periodicity is not a necessary condition to distinguish sound from noise. For two reasons:
the auditory system seems to tolerate small deviations from periodicity (if you wish to study this topic further, visit the page on perception of pitch);
no sound has a wave form that is exactly periodic. A periodic function has always been and will always be a given thing, while sound is something that is born, evolves over time and dies. After all, think of how boring a sound that was constantly the same would be!
Certainly, if there is no periodicity, not even remotely, in a sound phenomenon, it is merely noise. In this case, a sound wave has a continuous spectral content, made up of components of any frequency within a more or less wide band.
In fact, it is possible to produce examples of non-periodic waves that our ear considers to be a pleasant and consonant sound such as:
Graph
Spectrogram
Audio
rumore_armonico_2.wav
Harmonic noise. Bands include C2 C3 E♭4 G4 B♭4 C5. The width of each band is 2 Hz.
rumore_armonico_10.wav
Harmonic noise. Bands include C2 C3 E♭4 G4 B♭4 C5. The width of each band is 10 Hz.
rumore_armonico_20.wav
Harmonic noise. Bands include C2 C3 E♭4 G4 B♭4 C5. The width of each band is 20 Hz.
rumore_armonico_40.wav
Harmonic noise. Bands include C2 C3 E♭4 G4 B♭4 C5. The width of each band is 40 Hz.
rumore_armonico_100.wav
Harmonic noise. Bands include C2 C3 E♭4 G4 B♭4 C5. The width of each band is 100 Hz.
Harmonic noise is obtained by overlapping various bands of white noise, each of which is centred on the frequency of a note; in the examples above, the bands are centred on the notes of a C-E♭-G-B♭ chord over several octaves (66, 131, 311, 392, 466 and 523 Hz). When the bands are ideally very narrow, the spectrum becomes identical to that of a pleasant sound, while the wider the individual bands are, the more the character of noise takes over. In all cases, the resulting sound wave possesses periodic components but, in the strictest sense, it is never exactly periodic because a random component is always present, except in the limit of infinitely narrow bands.
Harmonic noise seems to reveal a fundamental characteristic of perception that conveys information by the degree of consonance or pleasantness of a sound wave. This information is of inestimable value to musicians. For more on this topic, see the pages on harmony and harmonic sounds and consonance and dissonance.
In conclusion
The examples show that the distinction between sound and noise does not depend on a single physical property of the wave. In general, we call sound a wave whose spectrum consists of a few well-separated components in (nearly) harmonic ratios, to which the ear assigns a definite pitch; we call noise a wave whose energy is spread continuously over wide frequency bands, to which no pitch can be assigned. Between the two extremes, however, there is a continuous gradation, as the harmonic noises show, and the final judgement also depends on perception: two periodic components too close in frequency, as in beats, give a "rough" sensation even though the wave is periodic.
Check your understanding
Is the superposition of two pure tones at 220 and 245 Hz a periodic wave? Why does it sound "rough"?Answer. Yes: both frequencies are multiples of 5 Hz, so the wave repeats every 1/5 of a second. The two frequencies, however, are too close for the ear to separate them: you hear a sound of intermediate pitch whose loudness oscillates 25 times a second (245 − 220 = 25 Hz), that is, a rapid beat, which we perceive as roughness.Does it make sense to ask whether a white noise is higher or lower than a sine wave at 220 Hz? Why?Answer. No. White noise has a uniform spectrum: it contains components of all audible frequencies with the same average intensity and has no periodicity, so the ear does not assign it a definite pitch to compare with that of the sine wave.In the harmonic noises of the table the width of the bands goes from 2 to 100 Hz. What changes in the spectrum and in the sound you hear?Answer. With narrow bands the spectrum is almost made of lines, like that of a chord, and you hear a pleasant sound of definite pitch. As the bands widen, the energy of each note is spread over an ever wider frequency interval, the wave becomes less and less regular and the character of noise takes over.Is the note of a real musical instrument an exactly periodic wave?Answer. No: a periodic function repeats identically for ever, while a note starts, evolves and dies away. It is nearly periodic only in its steady part. The ear tolerates these small deviations from periodicity and perceives them as a sound of definite pitch.
