SOUND WAVES. In every direction.

The first question is obvious: what is it? It is a longitudinal wave perceptible as sound. If it propagates in an elastic, continuous medium, it generates a local variation in pressure or density, which is transmitted in the form of a periodic sphere.

Variations in the pressure, humidity or temperature of the medium cause the molecules that make it up to move. Each of them transmits the vibration to the next, triggering a chain reaction. These coordinated actions of millions of molecules produce what are known as sound waves, which cause a sensation in the human ear that we call sound.

Sound is generated by longitudinal or compression elastic mechanical waves. This means that, in order to propagate, they need a medium (air, water, a solid body) that transmits the disturbance (it travels fastest in solids, then in liquids, more slowly still in air, and does not propagate in a vacuum). It is the medium itself that produces and enables propagation through its compression and expansion. For this to happen, it must be an elastic medium, since a completely rigid body does not allow vibrations to be transmitted.

They also travel in three dimensions, and their fronts in isotropic media are concentric spheres that radiate from the source of the disturbance in all directions. This is why they are spherical waves.

HUMAN PERCEPTION

The hertz (Hz) is the unit that expresses the number of vibrations emitted by a sound source per unit of time (frequency). The human ear is considered capable of perceiving sound waves with frequencies between 20 and 20,000 Hz, although ranges between 16 Hz (approximately the lowest note of a church organ: about 16.25 Hz) and 16,000 Hz (or 16 kHz) are also accepted. Waves with a frequency below the audible range are called infrasonic, and those above it ultrasonic.

The sensation of loudness is the human perception of the intensity of a sound. It is measured in a unit called the phon.

REFLECTION OF SOUND

When sound is reflected off a fixed obstacle, a wall for example, the magnitude of its velocity is conserved.

The laws of reflection also apply to its propagation. Only here we do not see them, but we do perceive them, above all when the wavelength of the vibration is smaller than the largest dimension of the flat object off which it is reflected.

If we were to observe what happens in a concert hall in which a door was left ajar, we would only be able to hear the bars played by a violin, or by any soloist, from certain positions, which would lie in the direction of the reflected sound.

CONSEQUENCES AND APPLICATIONS

The first and best known is reverberation (or echo). This phenomenon is due to the reflection of sound waves off a large obstacle, such as the wall of a large hall -without sound absorbers-, a rock face or a dense row of trees.

When the sound waves leaving the source strike the reflecting surface almost perpendicularly, the surface sends a brief sound back toward the source. If we accept that the persistence of auditory perception, after its cause has ceased, is in the order of a tenth of a second, 0.1 s, the minimum distance between the source and the reflecting wall that produces the echo must be such that the sound wave covers twice that distance in 0.1 s. Since the speed of sound in air at normal temperatures is about 340 m/s, echo can occur at distances above 17 m.

Its application in acoustics is based on this principle:

In auditoriums or theaters, the distance between the soloists or the conductors is greater, but the architecture of the halls must be designed so that the sound is absorbed by the walls, so that the volume of the hall behaves like an open space. Nor should this space exceed about thirty meters, so that the soloists' voices can be heard with sufficient power and clarity.

The design of the hall must meet two partly contradictory conditions:

• Good distribution of the sounds coming from the stage.

• A well-defined reverberation time. Reverberation is the prolongation of the sound perceived in the hall once the sound source has fallen silent, as a result of multiple non-simultaneous reflections off the surfaces of different walls.

A concert hall needs a fairly long reverberation (in the order of 2 seconds) for the sound to acquire sufficient splendor. A theater, however, cannot have a reverberation lasting more than 1 second. This can be fine-tuned with absorbent materials such as honeycomb panels, drapes, carpets, etc.

When the structure of the building was not conceived for listening to music, as in the case of cathedrals or many churches used as concert halls, the reverberation time is sometimes longer. There are well-known examples of good architectural design, such as the Golden Hall in Vienna, among others.

SHELLS OR ELLIPSES. BASIC CONCERT HALL ACOUSTICS

To improve the intelligibility of speech and music, elliptical reflectors are now built whose shape is reminiscent of certain open mollusk shells. The back of the loudspeaker is located at the focus of a hollow ellipsoid of revolution whose surface is perfectly polished. One of the properties of the ellipse is that if we draw straight lines to its foci from any point on the conic, these lines form equal angles with the normal to the ellipse. Consequently, every sound ray striking the ellipse is reflected through the second focus.

The loudspeaker is positioned so that its axis of symmetry coincides with that of the ellipse. In this way, the energy emitted by the shell is contained within a cone. A device such as this produces a significant directional effect and allows a listener to locate the source much better than with a normal loudspeaker, and it can also eliminate spurious reflections if the "shell" is oriented favorably.

The domes of opera houses and concert halls are ellipsoidal in shape.

The old prompter's boxes in theaters were also based on this principle: the prompter's voice stayed on stage without the audience being able to hear it.

REFRACTION OF SOUND

This is the change of direction a wave undergoes when passing from one medium to another. It only occurs if the wave strikes the boundary between the two media obliquely and if they have different refractive indices.

The refractive index is precisely the ratio between the speed in a reference medium (a vacuum, for electromagnetic waves) and the speed in the medium in question.

An example of this phenomenon can be seen when a pencil is dipped into a glass of water: the pencil appears to be broken. It also occurs when light passes through layers of air at different temperatures, on which the refractive index depends. Mirages are produced by an extreme case of refraction, called total reflection. Refraction is the deviation waves undergo in their direction of propagation when sound passes from one medium to a different one. Unlike in the phenomenon of reflection, in refraction the angle is no longer equal to the angle of incidence.

Refraction can also occur within the same medium when its characteristics are not homogeneous, for example when the temperature rises or falls from one point in the medium to another.

A clear example can be seen over a snow-covered surface. Under these conditions, sound is able to travel over long distances. This is due to the refractions produced beneath the snow, which is not a uniform medium. Each layer of snow has a different temperature. The deepest layers, which the sun does not reach, are colder than those at the surface. In these colder layers close to the ground, sound propagates more slowly.

Only harmonic waves have a well-defined velocity magnitude in a dispersive medium. In a medium of this kind, any other, non-harmonic vibration is distorted as it propagates.

At the boundary of a propagating medium, such as the surface of a wall, there is always partial reflection and refraction. Part of the sound energy is reflected off the wall, in accordance with the laws of reflection of spherical waves off a flat surface, with the angles of incidence and reflection being equal for each incident sound ray.

But another part of the sound is refracted into the wall, which also absorbs it, and only a small part of it is transmitted to the adjoining room after further partial reflection and refraction.

DIFFRACTION OF SOUND

This is a phenomenon that affects the propagation of sound. We speak of diffraction when, instead of continuing in its normal direction, sound spreads out in a continuous range of directions.

The explanation is found in Huygens' Principle, which states that any point on a wavefront can become a new source emitting frequencies identical to the one that gave rise to it. According to this principle, when the signal strikes an opening or an obstacle that blocks its propagation, all the points on its plane become secondary sources of waves, emitting new ones, called diffracted waves.

Diffraction can occur for two different reasons:

1. A sound wave encounters a small obstacle in its path and goes around it. Low frequencies are better able to bend around obstacles than high frequencies. This is possible because wavelengths in the audible spectrum lie between 3 cm and 12 m, so they are large enough to get past most of the obstacles they encounter.

2. A signal comes up against a small hole and passes through it.

The amount of diffraction will depend on the size of the opening itself and on the wavelength.

• If an opening is large compared with the wavelength, the diffraction effect is small. The sound propagates in straight lines or rays, like light.

• When it is smaller, the effects of diffraction are large and the sound behaves as if it were light coming from a point source located at the opening.

CONCLUSION

Applying very simple physical principles contributes much more to acoustics than one might imagine, and can help many readers find an explanation for certain phenomena that sometimes seem inexplicable. At CEC we are aware of the growing presence of all kinds of devices that do all the acoustic and setup work for us (Auddissey or similar). But although we professionals sometimes also rely on them initially, in the end it is our own ears that show us the way. And understanding how sound waves behave is where it all begins.