PHYSICS OF SOUND
The sound waves they are longitudinal mechanical waves, that is, the particles that transmit the waves vibrate in the direction of propagation of the wave. Mechanical waves are waves that propagate in deformable or elastic media.
They originate from the displacement of a portion of an elastic medium from its normal position, with subsequent oscillation around an equilibrium position.
Due to the elastic properties of the medium, the disturbance is transmitted from one layer to the next. The medium does not move, as a whole, following the movement of the wave: the various parts simply oscillate within restricted limits.
The ownership of the vehicle which determine the speed of a wave passing through it are its inertia and its elasticity:
• elasticity: generates restoring forces in every part of the medium, displaced from the equilibrium position;
• inertia: tells us how the part of the displaced vehicle will respond to the restoring forces.
The simplest wave that exists in nature is represented by a sinusoid on a diagram showing the displacement or time on the abscissae and the amplitude on the ordinate.
Characteristics of the wave
are the Frequency (f), the Wavelength, the Speed of propagation (c) and the Amplitude of the wave (A):
• frequency [Hz]: number of oscillations that occur in one second, is given by the inverse of the period (T), i.e. the time necessary to complete a complete oscillation;
• wavelength [m]: distance between two wave crests
• propagation speed [m/s]: distance traveled by the wave per unit of time. Its value for the propagation of sound in air in standard temperature, pressure and humidity conditions is 344 m/s;
• amplitude: maximum displacement, compared to the equilibrium condition, of the molecules that constitute the propagation medium. Therefore, as the amplitude increases, the intensity with which the sound is perceived increases.
Sound waves are generally generated by vibrating strings (e.g. violin, human vocal cords), by vibrating air columns (e.g. organ, smoke exhaust elements) and by vibrating membranes (e.g. drums, speakers). All these vibrating elements compress or rarefy the surrounding air which transmits these disturbances in the form of waves which move away from the source and hit the eardrum of the human ear generating the
sound sensation
. This sensation can be described for humans as:
• sounds: signals composed of a certain number of fixed and well-defined frequencies, i.e. a sum of waves having particular periodicity characteristics;
• noises: completely random phenomena made up of an infinite number of components, each with random amplitude and frequency.
THE
physical parameters that represent a sound
or a noise are the Sound pressure (p), the Acoustic power of the sound field (W) and the Intensity of the sound field (I):
• sound pressure [Pa]: value of the variation in atmospheric pressure caused by the acoustic disturbance, i.e. it is the difference between the pressure detected in a point in the presence of the sound event and the pressure in the same point in the absence of sound. Its reference value is equal to 20*10-6 Pa.
• sound power of the sound field [W]: the energy emitted by the sound source per unit of time;
• intensity of the sound field [W/m2]: average flow of energy which, in a unit of time, crosses a surface of unit area arranged perpendicular to the direction of propagation.
Any sound is determined once the intensity and frequency of its elementary components are known. The
decibels
allows you to quantify the intensity of the sound, taking into account the sound sensation, thanks to the measurement of the sound pressures, linked to the intensity, by the physical formula:
i = p2 / (pvh*c)
where pvh: density of the medium; c: speed of sound in the medium.
The sound pressure level, in decibels, is obtained from the formula, created by Fletcher:
L= 10*log(I/I0)= 20*log(p/p0)
where p0: reference value of sound pressure (equal to 2*10-5 N/m2).
To check the relationship between the sound sensation and the decibel it is appropriate to introduce the null sensation line and the normal Fletcher-Musson audiogram:
• zero sensation line: experimental curve in the plane, having the sound level on the ordinate and the frequencies on the abscissa. Indicates, as the frequencies vary, the hearing threshold varies;
•Fletcher-Musson audiogram: quadrant with the sound level on the ordinate and the frequencies on the abscissa and which contains a series of experimental curves which link, for the same sound sensations, the variation of the sound energy emitted to the variation of the frequencies. These curves are called isophone curves and allow us to better understand the link between the decibel measurement of pure sounds and their corresponding sound sensation.
Until now we have dealt exclusively with pure sounds, i.e. composed of a single vi
bration at any frequency. In reality, however, we are surrounded by complex sounds, composed of multiple simultaneous vibrations at different frequencies. In this case the relationship between the energy of the sound and its sonic sensation is more complex.
To reduce the energy spectrum in order to obtain meaningful measurements for the sound sensation, four are used weighting scales: A, B, C, D.
• The A, B, C scales: obtained from the Fletcher-Musson isophone curves of 40, 60, and 80 phon (unit of measurement dependent on the decibel). For this reason they weight the different frequencies by "cutting" from the spectrum the energy of sounds that would not be heard by our ear. In this way the measurements better reflect human sensation;
• the D scale: obtained following studies on the behavior of the human ear subjected to loud noises.
Scale A was applied to sounds of low intensity (about 50 dB), scales B and C to sounds of medium and high density. However, it has been demonstrated that this choice was unfounded, and the IEC 651 and IEC 804 regulations indicate the A scale as the one that best suits the measurement of sound sensation in normal environmental conditions, while the D scale is the most suitable for noises. from aeronautical traffic. Stairs B and C have fallen into disuse
.
Il fonometro è uno strumento che misura il livello di pressione sonora in decibel.
Dal punto di vista funzionale si può considerare il fonometro tradizionale come una scatola in cui entra, via microfono, una data pressione sonora ed esce la misura del livello sonoro. I fonometri tradizionali sono dotati di due circuiti di ponderazione: uno di frequenza ed uno dinamico, che controlla il tempo di risposta dello strumento (SLOW: 1 secondo; FAST: 125 millisecondi; IMPULSE: 35 millisecondi).
Il fonometro misura sempre il livello di pressione sonora globale ponderato dalle scale A, B, C, D.
With diction noise we mean acoustic vibration in the most general sense, regardless of the type and pleasantness of this vibration. Continuous noises can be constant intensity noises, pulse noises and variable intensity noises.
• vibrations of constant intensity: noises whose variability is within limits (variations in intensity greater than a couple of decibels);
• impulsive: mood whose intensity variation occurs very quickly, but not less than the brain's response time (35 milliseconds) and whose repetition occurs at a rate of less than 10 events per second. The auditory sensation of these noises is greater, with the same average intensity, compared to constant noises.
• variable: noise for which the change in sound level, having a difference of more than a couple of decibels, occurs in times longer than the average response time of the ear (about a tenth of a second).
It is necessary to clarify the concept of I disturb, which has a notable influence on the sound sensation. Acoustic disturbance is identified with sound input, that is, with the addition of sound vibrations to those pre-existing in the (background) environment.
The acoustic disturbance has the physical explanation in the covering effect of some sounds on others: low frequency sounds cover sounds at higher frequencies, but a high frequency sound does not cover lower frequency sounds.
Disturbance, however, occurs not only when the disturbing sound cancels out the existing sound, but also when the two sounds are heard at the same time.
Low frequency sounds introduced into an environment are by far the most disturbing of the entire spectrum.
The Prime Ministerial Decree of 1/3/91 defines residual and environmental noise in Annex A.
• residual noise level: equivalent continuous "A" weighted sound pressure level which is detected when specific disturbing sources are excluded;
• ambient noise level: produced by all noise sources existing in a given place and during a given period of time. It is made up of all the residual noise and that produced by the "specific disturbing sources";
•
background noise: it is not defined by law and is normally used to indicate residual noise.
After calculating the noise produced by the (point) source, it is necessary to calculate how this propagates into the surrounding space.
The sound that propagates outdoors it generally decreases in intensity as the distance between source and receptor increases. This attenuation (measured in dB) is the result of numerous mechanisms:
• attenuation caused by geometric divergence;
• attenuation due to the interposition of an obstacle between the source and the receptor;
• attenuation due to the absorption of acoustic energy by the air;
• attenuation caused by propagation on the ground.
The problem consists in calculating the sound level (L) of a source at a distance r from the source itself, based on data collected near the source.
The sound pressure level at a point far from the source is obtained by considering the known sound pressure level at some point near the source and subtracting from this level the total of all the attenuations taken one by one.
Sometimes, the known quantity is the sound power level. In that case, it comes first transformed into sound pressure level at a reference unit distance from the source, then it is replaced to obtain the sound pressure level.
Attenuation by non-directional point source divergence: it is the one which, in the absence of reflective surfaces, radiates sound waves uniformly in all directions. A sound source that is small in size compared to the wavelength of the sound it emits behaves like a point source.
The attenuation value can be obtained as follows:
L = Lref - 20 Log (r/r ref) [dB]
The sound level Lrif expressed in dB is known at a reference distance r with the suffix ref. The second term on the right-hand side in this equation represents the attenuation due to divergence:
Adiv = 20 Log (r/r ref) [dB]
The expression giving the sound pressure level at any distance, as a result of a sound source of sound power level LW, expressed in terms of the A-weighted sound power level, LWA is:
LA = LWA -20 Log r - 10.9 [dB(A)]
Attenuation by directional point source divergence:
source that radiates sound waves in all directions, but not equally.
Attenuation due to the presence of a reflective surface: a reflective plane significantly reduces the divergence of the sound from the source. The presence or absence of a reflecting plane does not influence the behavior of the sound source in producing sound.
To be a good sound reflector the surface of the reflecting plane must:
• be smooth and flat to minimize non-directional reflection of sound;
• be compact and non-porous.
Attenuation due to barriers: a barrier is a solid body that prevents the sight in a straight line source-receiver. A barrier attenuates the high-frequency components of the noise source more than the low-frequency components, resulting in a change in the resulting noise spectrum.
There are many design curves and rules of thumb that predict attenuation with a barrier: predicted attenuation values do not vary by more than 5 dB of each other. At a first estimate level, it can be stated that practically all solid barriers, if of appropriate geometry, can generate an attenuation of approximately 5 dB. With good design, 10 dB can be reached.
Attenuation due to a barrier is diminished by the downward bending of the sound path caused by downslope winds or temperature inversions common at night. Typically, these reductions are negligible when the receiver is relatively close to the barrier (distance less than 100 m) or when the wave path is deviated by an angle greater than 10 degrees.
Attenuation due to vegetation: trees and low vegetation (hedges, shrubs, undergrowth) are very ineffective barriers and provide little attenuation due to the screening effect: at frequencies below 1000 Hz their main contribution is not due to the barrier effect but rather due to excess attenuation. Typical values for ground effect attenuation are 5dB between 500 and 1000Hz at a distance of 5m and 10dB for distances greater than 10m.
Although vegetation can provide a good visual screen, it causes a screening effect only at high frequencies (above 2000 Hz) and for long distances.
To have appreciable barrier attenuation effects, the case must be very dense vegetation with broad leaves (corn field) and at large distances.
Attenuation by atmospheric absorption: When sound propagates in the atmosphere, its energy is converted into heat (atmospheric absorption). The attenuation of sound due to atmospheric absorption during propagation is given by:
Aatm = a * d/100 [dB]
where a: atmospheric attenuation coefficient per 100 m.
The attenuation coefficient depends mainly on the frequency and relative humidity and to a more moderate extent on the ambient temperature and pressure.
Sound absorption in air can be neglected at short distances from the source (distances less than a few hundred meters), with the exception of very high frequencies (above 5000 Hz). At large distances, where atmospheric attenuation is significant for all frequencies, the sound level should be calculated as a function of frequency for given conditions of temperature and relative humidity.
Propagation at great distances from the ground causes fluctuations in the instantaneous sound level arising from a stationary source with time constants ranging from tenths of a second to hours. The amplitude of these fluctuations increases with increasing distance from the source (reaching 10 dB for distances of hundreds or thousands of meters).
Attenuation due to ground effect: atmospheric conditions (especially wind and temperature) constitute an important influencing factor on the propagation of sound near the ground for horizontal distances greater than 50 m on open flat areas. The main effect is refraction, a change in the direction of sound waves.
Sound tends to propagate downward, when the propagation is downwind or during temperature inversions. Such downward refractive conditions are favorable for propagation, as they produce a minimum of excess attenuation. In the case of propagation on highly reflective surfaces, such as water, this minimum value approaches zero.
Sound refracts upward when propagation is upwind or during atmospheric thermal gradient conditions. The upward refraction produces a shadow area near the ground resulting in excess attenuation which reaches, as a typical value, 20 dB.
Propagation above the grass: Attenuation near the ground caused by the absorptive and reflective properties of the ground itself is called ground effect.
The trend of attenuation by propagation on a flat expanse of grass depends on the frequencies and the average height of the source and receiver above the ground:
[(hS hR)/2]
where S and R: subscripts of h.
Noise evaluation. Based on the Prime Ministerial Decree of 1.3.1991 which sets the maximum limits of exposure to noise in living environments and in the external environment, the acoustic sound pressure level is used to assess damage or disturbance from noise.
The Equivalent Level Leq represents an energy index, i.e. it expresses the average value of the sound energy perceived by an individual during a period of time.
To characterize environmental noise, descriptor parameters are used which also allow statistical analysis of the phenomenon. These parameters (cumulative statistical indices-Li) express the noise level exceeded in the percentage i of the observation time and allow characterizing conventional values such as peak noise, background noise and average noise.
• L1: noise level exceeded 1% of the observation time. Peak noise indicator;
• L10: noise level exceeded 10% of the observation time. Peak noise indicator;
• L50: noise level exceeded 50% of the observation time. Represents the average noise level;
• L90: noise level exceeded 50% of the observation time. Representative of background noise.
Prof. Dr. Eng. Ezio Rendina
Consulting & Management
Director
“Competent technician in environmental acoustics”
pursuant to Law 447/95 art. 2, paragraph 6