Sound

Sound is a mechanical vibration of a fluid, which propagates in the form of longitudinal waves thanks to the elastic deformation of this fluid. Human beings, like many animals, experience this vibration through the sense of hearing.

Acoustics is the science that studies sound; psychoacoustics studies how the organs of the human body feel and the human being perceives and interprets sounds.

Sound propagation

(A ‘pressure over time’ graph of a 20 ms recording of a clarinet tone demonstrates the two fundamental elements of sound: Pressure and Time. )

In a compressible fluid medium, a pressure variation propagates in the form of a wave. Sound does not propagate in a vacuum: matter is needed so that its vibration can propagate in sound waves. The air, in which humans live, is a favorable environment, and changes in air pressure constitute sound. The amplitude of the pressure variation is small compared to the static pressure (atmospheric pressure); for it to be perceptible, it must be sufficiently rapid and repeated.

A sound source is a vibrating object, such as a musical instrument or a loudspeaker, which causes air vibration. The disturbance propagates, but the air particles oscillate only a few micrometers around a stable position, in the same way as when throwing a stone in water, the waves move away from the point of. falls, but the water remains in the same place, it only moves vertically and not following the waves (a stopper placed on the water remains in the same position without moving). In fluids, the sound wave is longitudinal, that is, the particles vibrate parallel to the direction of travel of the wave.

Solids, by vibrating, can transmit sound. The vibration propagates there, as in fluids, with a weak oscillation of the atoms around their equilibrium position, resulting in a stress of the material, equivalent to the pressure in a fluid, but more difficult to measure. The rigidity of the material allows the transmission of transverse stress waves. Likewise, although to a lesser extent, the viscosity of a fluid can modify, particularly under extreme conditions, the propagation equations calculated for an ideal gas.

Speed

The speed of sound or the celerity of the sound depends on the nature, temperature and pressure of the medium.

The ideal gas mathematical model gives an approximate result for propagation in dry air. It results in a formula where the speed is proportional to the square root of the absolute temperature, in kelvins:

c_air = 20√T

For ordinary temperatures in inhabited places, the formula

c_air = 331.5 + 0.6 ∙ t_C ,

where t_C is the temperature in degrees Celsius, allows a quick calculation. The result of these two approximations deviates by less than 1 m/s from the speed of sound in dry air at normal atmospheric pressure between −25 and +35 °C calculated more precisely.

(Speed ​​of sound according to temperature and humidity)

The assimilation of dry air to an ideal gas leads to discrepancies with the measured values, particularly at high pressure and at low temperature. More precise or valid calculations over a wider range must consider the more complex relationships that exist in real gas.

The humidity of the air slightly increases the speed of sound. Hot air can contain more water vapor; the variation, exponential, is insensitive below 10 °C. At 30 °C, the speed of sound in air at 85% relative humidity is 2 m/s higher than in dry air.

The variation of the speed of sound in air is sometimes of considerable practical importance. In musical acoustics, this speed determines the frequency of the sound wave that comes out of a pipe resonating like an organ pipe. In laboratories, measuring the speed of sound under various conditions is one way of accessing characteristics of a material.

The speed of sound increases:

• when the density decreases (inertia effect);
• when elasticity or compressibility decreases (the ability to decrease in volume under the effect of compression).

In water, both much denser and much less compressible than air, the speed of sound is around 1500 m∙s⁻¹. In other environments, vibrations can spread even faster. In steel, the vibrations propagate from 5600 to 5900  m∙s⁻¹.

Intensity

The power of a spherical wave is distributed over a sphere, the area of ​​which is proportional to the square of the radius. As a result, the sound power per unit area decreases in proportion to the square of the distance to the source, if there are no obstacles deflecting the sound.

Most of the time, absorption attenuation in the propagation medium varies with frequency. In the air, at 500 m, the amplitude of a wave at 8000 Hz is ten times more weakened than a wave at low frequency. Only certain causes are known. The viscosity of the air causes an attenuation proportional to the square of the frequency; thermal exchanges cause additional attenuation, proportional to the frequency and variable according to the composition of the air, in particular according to its humidity. The measurement shows additional attenuation that has not been incorporated into theoretical models.

The study of the propagation in a given place is done from the sound pressure, which expresses the sound power. It is often expressed in decibels in relation to the limit of perception, or from the acoustic intensity, which expresses the quantity and direction of the power which is transferred by the vibration of the medium. We thus build a mathematical model of the acoustic field.

In the air

Atmospheric and meteorological conditions influence local and long-range acoustic propagation.

To predict the propagation of sound, it is necessary to know the average temperature, but also the thermal structure and the hygrometry of the air mass crossed as well as the direction of the wind.

• The sound propagates less well horizontally than at rising angles because of the change in density. The design of open-air theaters since ancient times has taken this property into account.
• A low inversion layer forms a temperature gradient which deflects rising waves by refraction towards the ground, acting as a waveguide which carries sound. For example, following the night cooling, it is possible to hear a train 5 km from a downwind railway line despite obstacles.
• Humidity increases the natural speed of sound.
• Attenuation is much less downwind as long as its ground speed is not too turbulent.
• Wind speed increases with height above ground. This wind gradient layers the sound wave which propagates in the direction of the wind, pushing it towards the ground. Conversely, the wave traveling against the wind is heard much less on the ground, because the same gradient deflects it towards the sky.

In heterogeneous environments

The presence of water droplets in the atmosphere, such as in clouds and mists, such as ice crystals, in snowy conditions, dramatically changes the propagation of sound. It results in a decrease and a dispersion of the speed and an attenuation all the more marked as the frequency is low.

In heterogeneous environments, the sound undergoes reflections and refractions on the interfaces, which lead to diffusions and absorptions which are the basis of sound insulation.

Thunder

The speed of sound can be rounded off to one kilometer every three seconds in order to calculate quite easily, although approximately, the distance between the observer and a lightning bolt during a thunderstorm. Indeed, the flashes are sufficiently close so that we can consider perceiving the light instantly. Each three-second period that you then have to wait to hear the thunder is therefore roughly one kilometer. Thus, for a wait of 8 seconds, the distance which separates the observer from the flash is 8 × 340 = 2720 m; or, more simply 2 kilometers two thirds.

Given the estimation method, more precision is illusory. Even disregarding human reaction time (if one counted, for example, the elapsed time on a video recording), it is unlikely that in an atmosphere disturbed by high winds and considerable temperature and humidity differences the sound wave always travels in a straight line and at the same speed.