Hi there! In this issue we will talk about the sound and its propagation in the air.

Let's analyze all the sound propagation features:

Every sound, once generated by a vibrating elastic body, is transmitted through the surrounding medium, creating a series of waves where particles the medium is composed of are subject to condensation and rarefaction. It could seem pretty obvious, but it's better to point out that a mean of conduction is essential for sound transmission. No transmission is possible in vacuum, differently to what happens for light transmission.

Here we are with some frequency values and relevant wavelengths (for waves propagating through air):

It's worth to remind that the wavelength can be determined by considering the distance between its crests (i.e. between two consequent maxima or two consequent minima).

The maximum amount of particle displacement is called vibration amplitude. As soon as we go away from the perturbation source, then vibration amplitude decreases, because of the damping factor, therefore the particles gradually get back to their original static equilibrium position (due to the g-force).

The physic propagation can occur in different ways, for instance:

• transversal: where propagation starts from the source on a plane, following all the half lines departing from it
• longitudinal: oscillations transmitted by the particles go in the propagation direction, that is, from the source following the relative half line

Transversal and longitudinal waves are two simplified limit cases of mechanical waves, which are in general more complex phenomena. Now, let's talk about our main interest, that is, the wave propagation through spherical waves.

• with spherical waves, propagation starts from a given point in the space along all the half lines generated by the source.

As far as waves propagation is concerned, there are also some particular features to take into account:

1. the sound intensity as perceived is inversely proportional to the square root of the distance from the source

2. the sound intensity is modified if turbulences are present

3. both intensity and speed of sound are determined by the conductive medium density

4. the speed of sound does not depend on its frequency nor its intensity

Let's see how the speed of sound changes according to the conducting media.

In dry air, the speed of sound is about 344 meters per second (at 20°C and sea level)

The speed is then 1480m/s in water, 3350m/s in wood, 3400m/s in cement, 5050m/s in steel and 5200m/s in glass

As we can easily notice from the different speed details, the stronger the conducting medium is, the faster the propagating speed is.

In the next issue we will analyze the connection between environment and waves.

Bye!

Last time we talked about the simple sound and its features.

The sound we usually hear is not a simple one (sinusoidal oscillation), but a complex sound.

In order to treat this issue, it is necessary to clarify the concept of envelope (we will study this argument in deep later) and harmonics.

The sound envelope is the variation of its amplitude over time.

Let's consider now an instrumental sound: his complexity is evident. If you listen to just a single note, you will find out how the sound is made up, not only of an oscillation, but also of a changeable number of "elements". Those elements are the harmonics we are talking about.

Harmonics show well defined relationship between themselves, and with the fundamental oscillation.

Our definition of a complex sound will thus be:

A periodic oscillation constituted by a fundamental frequency and a series of other frequencies which are integer multiples of the fundamental, and are named higher order harmonics.

This definition naturally leads to the Fourier theorem: “Every periodic function, anyhow complex, can be represented as a (weighted) sum of simple sinusoidal functions whose frequencies are integer multiples of a fundamental frequency”.

So, every harmonics has its own frequency, but also its own amplitude and phase, which are completely independent with respect to the fundamental component. It's indeed the number of harmonics and the parameters of each of them which determines the character of a complex sound that is its timbre.

Complex sounds may be composed of a varying number and kind of harmonics. They can have more or less, even and/or odd harmonics.

Let's look at the harmonics series starting from C2 (about 66Hz). As one can see from the example, the harmonics which are generated have well defined frequency intervals. Starting from 66Hz (C2) we find 132Hz (C3 - octave), 198Hz (G3), 264Hz (C4) and so on.

We may now define the interval which is mainly a musical concept, but may be defined also in a physical framework. The interval is the pitch difference between two sounds, whose value is represented by a ratio between their frequencies.

We may say, at this point, that both the kind and the number of harmonics contained in an instrumental sound depend on the shape of the instrument and the materials it is built of: thus we may give a first definition of a sound TIMBRE as depending (from a physical point of view) on the kind and number of harmonics added to the fundamental one, on their amplitude and phase.

Let's see now some practical examples of complex sounds. 

The Hammond organ works exactly in this way, by generating a fundamental sound plus even and odd harmonics which can be managed through the Drawbars.

The "classical" waves of our synthesizers (triangle, sawtooth, pulse) are nothing else than complex sounds formed by different harmonics. Let's look at them one at the time:

Square Wave

Only odd harmonics are present, whose amplitude is proportional to their order, so the second component (third harmonics) has an amplitude which is one third of the fundamental, and so on. They are all in phase.

Triangle Wave

Only odd harmonics are present, and they are in counter-phase. Their amplitude is proportional to the square of their order. This means that the second component (third harmonics) has an amplitude which is one ninth of the fundamental, and so on.

Sawtooth Wave

There are both even and odd harmonics, they are in phase and their amplitude is proportional to the harmonics order, so that the second harmonics has an amplitude which is half the amplitude of the fundamental and so on.

In order to obtain a reversed sawtooth one should simply change the harmonics phase (counter-phase)

This seems very complex, but one simply has to sum up all the components and the fundamental to obtain the resulting wave.

The acoustic instruments sound is a complex sound itself. But, compared to the sounds seen above, they also show a number of inharmonic components, due to the instrument features. For example, the noise of a grand piano hammer beating up a string, or that of a bow sliding on a violin strings are examples od inharmonic components.

We will treat all these things in the next issues.