By Federico Miyara


Sound Waves

Sound is created by a disturbance travelling in an elastic medium. For instance, when an excess pressure is produced on some region of the air, that region tends to expand towards the neighbouring zones. This, in turn, compresses those zones, creating a new excess pressure which will tend to expand next, and, again, a new excess pressure is further created. The pressure disturbance will thus propagate through the air, and eventually it will reach some receiver (for instance a microphone or an ear). Excess pressure is called sound pressure.

This kind of movement in which it is not the medium itself but some disturbance what is travelling, is called a wave. There are many other types of waves, such as radio waves, light, heat radiation, the ripples on the surface of a lake, tsunamis, earthquakes, etc. When the wave takes place in a liquid or gaseous medium (except surface waves), the wave is called an acoustic wave. When a wave is audible, it is called a sound wave.

A particularly important point regarding waves is that there are some features which keep almost unchanged along the wave's path, for instance the wave shape or its total energy (provided the medium is not dissipative).

Acoustic waves travel usually at a given constant speed, which depends on the medium and environmental conditions such as temperature. At ambient temperature, the speed of sound in air is

c = 345 m/s .

This means that it takes one second for sound to go over a 345-meter distance. In water sound travels more than 4 times faster than in air. When there are temperature gradients, such as it happens between points hundreds of meters apart, or at different heigts, the speed of sound changes along its path, making the path a curve rather than a straight line. This is the reason why our perecption is fooled when we try to find out where an airplane is just by its sound.

Periodic waves

We introduced the concept of wave propagation by means of a single disturbance of a medium. Actually, most waves are the result of many succesive disturbances of the medium, instead of only one. When those disturbances are generated at regular intervals and are all the same shape we are in the presence of a periodic wave, and the number of disturbances per unit time is called the frequency of the wave. It is expressed in a unit called Hertz (Hz), meaning cycles per second (a cycle is all that happens in between a disturbance). In the case of sound waves, frequency is between 20 Hz and 20,000 Hz. Acoustic waves of frequency smaller than 20 Hz are called infrasounds, and those of frequency greater than 20,000 Hz are called ultrasounds. Neither of them can ordinarily been heard by humans. Several animals (such as the dog, for instance) can hear very low frequency sounds, such as those created by ground waves during an earthquake. This is the reason why animals go mad when an earthquake is about to take place: they can hear the "warning" signal we cannot. Similarly, animals usually can hear ultrasounds. Bats are a remarkable case: they can hear above 100,000 Hz, which allows them to orientate by means of sound signals, using a principle known as sonar (similar to the popular radar).

Aperiodic waves

Even if there are many sounds which are nearly periodic, such as those sounds produced by pitched musical instruments, the vast majority of sounds in Nature are aperiodic, that is, succesive disturbances are not equally spaced in time, and are not of constant shape either. This is what in a technical sense is called noise. Aperiodic waves usually cannot convey the sensation of pitch. Some examples are the consonants of speech, urban noise, the noise of the wind and the sea, and the sound of many percussive instruments such as drums, charlestons, etc.


Spectrum is a central concept in Acoustics. When we introduced the concept of frequency, we said that periodic waves have an associated frequency. This is only part of the truth, however, since usually they have several frequencies at the same time. This is because a noteworthy mathematical theorem called Fourier's Theorem (after the French mathematician Fourier, who discovered it), which states that any periodic waveshape may be alternatively created by superposing different waves of a special shape called sine wave (or sinusoid), each of which has a frequency that is an integer multiple of the frequency of the original wave. So, when we hear a 100 Hz sound, we are actually hearing sine waves of frequencies 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz and so on. These sine waves are called the harmonics of the original sound, and they happen to be clearly audible in certain musical instruments, such as the guitar.

What about an original sound whose shape is already a sinusoid? When one tries to apply Fourier's theorem to a sinusoid, the result is that has a single harmonic of the same frequency as the original sinusoid, to be sure. (Note that Fourier's theorem does not say that all waveshapes must have several harmonics, but rather that any waveshape can be obtained as a superposition of a number of sinusoids, which might happen to be only one (as a matter of fact this is the case for a sinusoid!) The fact that each sine wave has a single frequency is the reason why sine waves are also called pure tones.

The description of the sine waves which compose a given sound is called the spectrum of the sound. The spectrum of sound is important for several reasons. First, because it allows a description of sound waves which is closely related to the effect of different devices and physical modifiers of sound. In other words, if one knows the spectrum of a given sound, one can find out how it will be affected by, say, the absorptive properties of a thick carpet. The same is not true if one only knows its wave shape.

Second, spectrum is important also because the aditory perception of sound is predominantly spectral in nature. In other words, before performing any further processing of the auditory signal our ears breake the incoming sound into its frequency components, i.e., the sine waves which, according to Fourier's theorem, form that sound. That is the reason why whith a little practice one can easily guess the notes which make up a chord.

What about aperiodic sounds' spectra? Fourier's theorem can be extended to the case of aperiodic sounds. Aperiodic sounds may be as simple as bell-like sounds, or as complex as the so-called white noise (the noise captured by an FM receiver when there is no signal nor carrier). In the first case, we can manage to obtain a series of discrete (i.e., separate) frequencies even if their frequencies will no longer be integer multiples of anything. We might have for instance 100 Hz, 143.3 Hz, 227.1 Hz, 631.02 Hz. In the second case, we have... all frequencies! This is what is called a continuous spectrum.

Sound Intensity

Why are some sounds louder than others? There are many reasons, but the main one is traceable to the amplitude of sound waves. The amplitude of a sound wave is the maximum excess pressure of the sound wave in each cycle. In the case of noise, the amplitud may be continuously changing, and it is customary to compute some sort of average. There are several approaches to the analysis of loudness, which may be found in the accompanying document on Sound Levels.


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