.. _acoustical_explanation-part: .. role:: underline :class: underline ======================================== Explanation of Acoustical Principles ======================================== Introduction --------------- | The purpose of this page is to present and explain the different acoustic principles used in Code_TYMPAN. | But also to show the consistency of the theoretical results and those of Code_TYMPAN using simple models. Model --------------- Model description ~~~~~~~~~~~~~~~~~ .. image:: _static/built_resources/Model_case_0.png :align: center | The reference model consists of a source and a receiver without any obstacle or object around but with a ground. +------------+-------+-------+-------+-------+ | Name | Pos X | Pos Y | Pos Z | Units | +============+=======+=======+=======+=======+ | Source | -50 | 0 | 2 | m | +------------+-------+-------+-------+-------+ | Receiver | 50 | 0 | 2 | m | +------------+-------+-------+-------+-------+ +-----------------+---------+-------+---------------------------------------+ | Symbol | Value | Units | Comment | +=================+=========+=======+=======================================+ | Distance S/R | 100 | m | | +-----------------+---------+-------+---------------------------------------+ | Distance ref | 1 | m | | +-----------------+---------+-------+---------------------------------------+ | Source height | 2 | m | | +-----------------+---------+-------+---------------------------------------+ | Receiver height | 2 | m | | +-----------------+---------+-------+---------------------------------------+ | dp | 100 | m | distance S->R Projected on the ground | +-----------------+---------+-------+---------------------------------------+ Calculation parameters for 3 reference modelizations ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ All acoustic calculations were carried out under homogeneous conditions. :underline:`Ground reflection case without screen` Model 1 : acoustic propagation with ground reflection and without screen +--------------+-------------+-------+------------------------------------------------------------------------------------------+ | Symbol | Value | Units | Comment | +==============+=============+=======+==========================================================================================+ | Gs | 0 | | ground factor 9613-2 source region | +--------------+-------------+-------+------------------------------------------------------------------------------------------+ | Gr | 0 | | ground factor 9613-2 receiver region | +--------------+-------------+-------+------------------------------------------------------------------------------------------+ | Gm | 0 | | ground factor 9613-2 intermediate region | +--------------+-------------+-------+------------------------------------------------------------------------------------------+ | σe | 20000 | | kRayls, flow resistivity | +--------------+-------------+-------+------------------------------------------------------------------------------------------+ | e | 1 | m | ground thickness | +--------------+-------------+-------+------------------------------------------------------------------------------------------+ | dp1 | 50 | m | ground distance source -> reflection point; Descartes' law: tan β = hs/dp1 = hr/(dp-dp1) | +--------------+-------------+-------+------------------------------------------------------------------------------------------+ | cos β | 0.999200959 | | cosine of the ground reflection angle | +--------------+-------------+-------+------------------------------------------------------------------------------------------+ | sin β | 0.03996803 | | | +--------------+-------------+-------+------------------------------------------------------------------------------------------+ | length | 100.079968 | m | reflected path length | +--------------+-------------+-------+------------------------------------------------------------------------------------------+ :underline:`Screen case` .. image:: _static/built_resources/Model_case_1.png :align: center Model 2 : acoustic propagation with ground reflection and thin screen between the source and the receiver +------------------------+-----------------------+-------+------------------+ | Name | Value | Units | Comment | +========================+=======================+=======+==================+ | Single thin screen | | | | +------------------------+-----------------------+-------+------------------+ | Position | (-25, 10) à (-25,-10) | | | +------------------------+-----------------------+-------+------------------+ | Screen/source distance | 25 | m | | +------------------------+-----------------------+-------+------------------+ | Screen height | 8 | m | | +------------------------+-----------------------+-------+------------------+ | e | 0.3 | m | screen thickness | +------------------------+-----------------------+-------+------------------+ :underline:`9613-2 calculation parameters` +--------------+---------+-------+-----------------------------------------------------------------------------------------------------------+ | Symbol | Value | Units | Comment | +==============+=========+=======+===========================================================================================================+ | a* | 0 | m | component of the distance parallel to the edge of the screen between the source and the receiver (9613-2) | +--------------+---------+-------+-----------------------------------------------------------------------------------------------------------+ | ll | 10 | m | perpendicular horizontal dimension SR left | +--------------+---------+-------+-----------------------------------------------------------------------------------------------------------+ | lr | 10 | m | horizontal dimension perpendicular SR right | +--------------+---------+-------+-----------------------------------------------------------------------------------------------------------+ | dSS,top | 25.71 | m | distance between the source and the first diffraction edge for the vertical path | +--------------+---------+-------+-----------------------------------------------------------------------------------------------------------+ | dSR,top | 75.24 | m | distance between the second diffraction edge and the receiver for the vertical path | +--------------+---------+-------+-----------------------------------------------------------------------------------------------------------+ | dSS,lat | 26.93 | m | distance between source and first diffraction edge for side paths | +--------------+---------+-------+-----------------------------------------------------------------------------------------------------------+ | dSR,lat | 75.66 | m | distance between second diffraction ridge and receiver for side paths | +--------------+---------+-------+-----------------------------------------------------------------------------------------------------------+ .. note:: The component a corresponds to the component of the distance along the y axis. In our example, it is zero, but in general it is not. :underline:`Reflection case` .. image:: _static/built_resources/Model_case_2.png :align: center +--------------+----------------------+-------+--------------------------------------------+ | Name | Value | Units | Comment | +==============+======================+=======+============================================+ | Position | (-52,10) à (-52,-10) | | | +--------------+----------------------+-------+--------------------------------------------+ | β_reflex | 0.0 | rad | angle of incidence | +--------------+----------------------+-------+--------------------------------------------+ | ρ_reflex | 1.0 | | acoustic reflection coefficient | +--------------+----------------------+-------+--------------------------------------------+ | l_min | 8.0 | m | minimum reflective length dimension | +--------------+----------------------+-------+--------------------------------------------+ | dS,O | 1.85 | m | source distance to reflection point | +--------------+----------------------+-------+--------------------------------------------+ | dO,R | 101.85 | m | distance from reflection point to receiver | +--------------+----------------------+-------+--------------------------------------------+ | DIr | 0 | | source directivity index -> receiver image | +--------------+----------------------+-------+--------------------------------------------+ Acoustic ~~~~~~~~~~~~~~~~ +--------------+-------------------+--------------+--------------+--------------+ | Source spectrum | Source directivity | +--------------+-------------------+--------------+--------------+--------------+ | Frequency | Lw(fc) dB re 1 pW | W(fc) W | Module | Phase | +==============+===================+==============+==============+==============+ | 16 Hz | 0 | 1E-12 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 20 Hz | 0 | 1E-12 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 25 Hz | 0 | 1E-12 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 31.5 Hz | 0 | 1E-12 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 40 Hz | 0 | 1E-12 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 50 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 63 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 80 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 100 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 125 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 160 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 200 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 250 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 315 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 400 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 500 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 630 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 800 Hz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 1 kHz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 1.25 kHz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 1.6 kHz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 2 kHz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 2.5 kHz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 3.15 kHz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 4 kHz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 5 kHz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 6.3 kHz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 8 kHz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 10 kHz | 80 | 0.0001 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 12.5 kHz | 0 | 1E-12 | 1 | 0 | +--------------+-------------------+--------------+--------------+--------------+ | 16 kHz | 0 | 1E-12 | | | +--------------+-------------------+--------------+--------------+--------------+ +--------------+-------------------+--------------+--------------+--------------+ | Lw | 93.80 | dB | | | +--------------+-------------------+--------------+--------------+--------------+ Atmospheric absorption ---------------------- This part details the global and model-specific parameters for the calculation of atmospheric absorption Weather parameters ~~~~~~~~~~~~~~~~~~ +--------------------------------+---------+--------------------------------------------------------------------------+ | Symbol | Value | Physical values | +================================+=========+==========================================================================+ | R | 8.31441 | Ideal gas constant | +--------------------------------+---------+--------------------------------------------------------------------------+ | Absolute_zero | 273.15 | Temperature 0°C in K | +--------------------------------+---------+--------------------------------------------------------------------------+ | M | 0.029 | Molar mass of air | +--------------------------------+---------+--------------------------------------------------------------------------+ | y | 1.41 | Ratio of the specific heats respectively at constant pressure and volume | +--------------------------------+---------+--------------------------------------------------------------------------+ | Reference atmospheric pressure | 101325 | Pa | +--------------------------------+---------+--------------------------------------------------------------------------+ | Reference sound pressure | 293.15 | K | +--------------------------------+---------+--------------------------------------------------------------------------+ | Reference sound pressure | 0.00002 | Pa | +--------------------------------+---------+--------------------------------------------------------------------------+ | Reference sound power | 1E-12 | W | +--------------------------------+---------+--------------------------------------------------------------------------+ :underline:`Specific model` +--------------+---------+------------------------+ | Symbol | Value | Units | +==============+=========+========================+ | Temperature | 20 | °C | +--------------+---------+------------------------+ | Pressure | 101325 | Pa | +--------------+---------+------------------------+ | Hygrometry | 70 | % humidity in the air | +--------------+---------+------------------------+ Atmospheric attenuation calculation ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | Atmospheric attenuation comes from molecular relaxation phenomena on the path of the wave. | It is proportional to the distance and depends on the conditions of temperature, pressure and relative humidity of the air. Atmospheric attenuation in Iso 9613-1 Standard ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | The attenuation by atmospheric absorption is given by: .. image:: _static/built_resources/Attenuation_1.png :align: center | With f the frequency, i the initial point, t the point considered and s the sound propagation distance in m. | α is the pure sound attenuation coefficient in decibels per meter. Atmospheric attenuation in default Solver ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | Calculations up to atmospheric absorption strictly identical to what is in the standard | Calculation of attenuation according to the formula below applied by frequency third octav. .. image:: _static/built_resources/Attenuation_2.png :align: center Atmospheric attenuation in Code_TYMPAN ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The calculations are identical to the note of the default solver. Note that in the Code_Code_TYMPAN implementation: * Modulus and phase calculation for each Aatmi third octav band. * The calculation being made in spectrum of p²(fc), the attenuation is squared. Implementation ~~~~~~~~~~~~~~~~ * void AtmosphericConditions::compute_absorption_spectrum(): Calculates the atmospheric absorption spectrum α for the weather conditions of the model. * AtmosphericConditions::compute_length_absorption(double length) const: Returns the atmospheric attenuation spectrum in explicit state (physical quantity), corresponds to the Aatmi(f) of the DefaultSolver. * void TYChemin::calcAttenuation(const TYTabEtape& tabEtapes, const AtmosphericConditions& atmos): Calculates the atmospheric attenuation from the power spectrum of the source taking into account the directivity and as a function of the path length. .. image:: _static/built_resources/Attenuation_3.png :align: center * OSpectre TYTrajet::getPEnergetique(const AtmosphericConditions& atmos): Calculates the squared sound pressure spectrum, p²(fc). In energy, p²(fc) = W(fc)*divGeom*Aatmi(fc)² Atmospheric calculation ----------------------- | The objective is to present the calculation of the various parameters of atmospheric attenuation based on what is implemented in Code_Code_TYMPAN. | The calculation proposed below relates to a specific use case described in the "Model" and "Weather" parts. Sound celerity calculation, c ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +---------+---------+--------+-----------------------+ | Symbol | Value | Units | Comment | +=========+=========+========+=======================+ | tk | 293.15 | K | Temperature in Kelvin | +---------+---------+--------+-----------------------+ | c | 344.25 | m/s | Sound speed | +---------+---------+--------+-----------------------+ | In Code_TYMPAN : | double AtmosphericConditions::compute_c() const Impedance calculation ~~~~~~~~~~~~~~~~~~~~~ +---------+---------+-----------+----------------------------------------------------------------------+ | Symbol | Value | Units | Comment | +=========+=========+===========+======================================================================+ | ρ | 1.21 | kg.m-3 | Air density | +---------+---------+-----------+----------------------------------------------------------------------+ | z | 415.02 | kg.m-2s-1 | acoustic specific characteristic impedance. Usually denoted z0 = ρ*c | +---------+---------+-----------+----------------------------------------------------------------------+ .. note:: In Code_TYMPAN ρ, the density of air, is calculated from the molar mass of air M and the weather conditions according to the following ideal gas formula: ρ = PM / RT | In Code_TYMPAN : | double AtmosphericConditions::compute_z() Atmospheric absorption ~~~~~~~~~~~~~~~~~~~~~~ :underline:`Mole fraction of water vapor` +-------------------+--------------+-------+-----------------------------------------------------------------+ | Symbol | Value | Units | Comment | +===================+==============+=======+=================================================================+ | T01 | 273.16 | K | Isothermal temperature at the triple point | +-------------------+--------------+-------+-----------------------------------------------------------------+ | Relative pressure | 1 | Pa/Pa | Relative pressure | +-------------------+--------------+-------+-----------------------------------------------------------------+ | C | -1.63712658 | | Exponent C, see Appendix B2 ISO 9613-1, dimensionless quantity | +-------------------+--------------+-------+-----------------------------------------------------------------+ | Psat | 2336.630453 | Pa | Saturating vapor pressure | +-------------------+--------------+-------+-----------------------------------------------------------------+ | h molar | 1.614252472 | % | Mole fraction of water vapor | +-------------------+--------------+-------+-----------------------------------------------------------------+ | In Code_TYMPAN : | double AtmosphericConditions::compute_hm() const :underline:`Atmospheric absorption spectrum` +------------+--------------+-------+-------------------------------+ | Symbol | Value | Units | Comment | +============+==============+=======+===============================+ | frO | 53173.95674 | Hz | Oxygen relaxation frequency | +------------+--------------+-------+-------------------------------+ | frn | 460.9906921 | Hz | Nitrogen relaxation frequency | +------------+--------------+-------+-------------------------------+ +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | Frequency | Order | Exact frequency | f² | α (dB.m-1) | k (m-1) | | | | | | atmospheric absorption coefficient | acoustic wave number | +==============+=============+=================+==============+=====================================+========================+ | 16 Hz | 0 | 15.8 | 251.2 | 5.75329E-06 | 0.289273495 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 20 Hz | 1 | 20.0 | 398.1 | 9.11237E-06 | 0.364173754 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 25 Hz | 2 | 25.1 | 631.0 | 1.44272E-05 | 0.458467594 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 31.5 Hz | 3 | 31.6 | 1000.0 | 2.2828E-05 | 0.577176504 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 40 Hz | 4 | 39.8 | 1584.9 | 3.60861E-05 | 0.726622168 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 50 Hz | 5 | 50.1 | 2511.9 | 5.69587E-05 | 0.914763112 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 63 Hz | 6 | 63.1 | 3981.1 | 8.96923E-05 | 1.151618528 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 80 Hz | 7 | 79.4 | 6309.6 | 0.000140718 | 1.449801829 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 100 Hz | 8 | 100.0 | 10000.0 | 0.000219517 | 1.825192365 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 125 Hz | 9 | 125.9 | 15848.9 | 0.000339472 | 2.29778105 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 160 Hz | 10 | 158.5 | 25118.9 | 0.000518179 | 2.892734954 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 200 Hz | 11 | 199.5 | 39810.7 | 0.000776135 | 3.641737544 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 250 Hz | 12 | 251.1 | 63095.7 | 0.001132366 | 4.584675937 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 315 Hz | 13 | 316.2 | 100000.0 | 0.001596482 | 5.771765042 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 400 Hz | 14 | 398.1 | 158489.3 | 0.002160413 | 7.266221682 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 500 Hz | 15 | 501.2 | 251188.6 | 0.002797920 | 9.147631123 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 630 Hz | 16 | 631.0 | 398107.2 | 0.003478850 | 11.51618528 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 800 Hz | 17 | 794.3 | 630957.3 | 0.004194039 | 14.49801829 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 1 kHz | 18 | 1000.0 | 1000000.0 | 0.004977810 | 18.25192365 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 1.25 kHz | 19 | 1258.9 | 1584893.2 | 0.005921435 | 22.9778105 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 1.6 kHz | 20 | 1584.9 | 2511886.4 | 0.007184447 | 28.92734954 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 2 kHz | 21 | 1995.3 | 3981071.7 | 0.009016418 | 36.41737544 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 2.5 kHz | 22 | 2511.9 | 6309573.4 | 0.011800116 | 45.84675937 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 3.15 kHz | 23 | 3162.3 | 10000000.0 | 0.016125980 | 57.71765042 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 4 kHz | 24 | 3981.1 | 15848931.9 | 0.022911167 | 72.66221682 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 5 kHz | 25 | 5011.9 | 25118864.3 | 0.033582957 | 91.47631123 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 6.3 kHz | 26 | 6309.6 | 39810717.1 | 0.050353926 | 115.1618528 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 8 kHz | 27 | 7943.3 | 63095734.4 | 0.076620551 | 144.9801829 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 10 kHz | 28 | 10000.0 | 100000000.0 | 0.117507392 | 182.5192365 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 12.5 kHz | 29 | 12589.3 | 158489319.2 | 0.180531919 | 229.778105 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | 16 kHz | 30 | 15848.9 | 251188643.2 | 0.276238144 | 289.2734954 | +--------------+-------------+-----------------+--------------+-------------------------------------+------------------------+ | In Code_TYMPAN : | void AtmosphericConditions::compute_absorption_spectrum(), calcule le spectre d'absorption atmosphérique α. | void AtmosphericConditions::compute_k(), calcule le spectre du nombre d'onde k. :underline:`Atmospheric attenuation` +--------------+-------------+--------------+ | | Aatmos | +--------------+-------------+--------------+ | Frequency | | | +==============+=============+==============+ | 16 Hz | 0.999934 | 28.927350 | +--------------+-------------+--------------+ | 20 Hz | 0.999895 | 36.417375 | +--------------+-------------+--------------+ | 25 Hz | 0.999834 | 45.846759 | +--------------+-------------+--------------+ | 31.5 Hz | 0.999737 | 57.717650 | +--------------+-------------+--------------+ | 40 Hz | 0.999585 | 72.662217 | +--------------+-------------+--------------+ | 50 Hz | 0.999344 | 91.476311 | +--------------+-------------+--------------+ | 63 Hz | 0.998968 | 115.161853 | +--------------+-------------+--------------+ | 80 Hz | 0.998381 | 144.980183 | +--------------+-------------+--------------+ | 100 Hz | 0.997476 | 182.519237 | +--------------+-------------+--------------+ | 125 Hz | 0.996099 | 229.778105 | +--------------+-------------+--------------+ | 160 Hz | 0.994052 | 289.273495 | +--------------+-------------+--------------+ | 200 Hz | 0.991104 | 364.173754 | +--------------+-------------+--------------+ | 250 Hz | 0.987048 | 458.467594 | +--------------+-------------+--------------+ | 315 Hz | 0.981788 | 577.176504 | +--------------+-------------+--------------+ | 400 Hz | 0.975434 | 726.622168 | +--------------+-------------+--------------+ | 500 Hz | 0.968301 | 914.763112 | +--------------+-------------+--------------+ | 630 Hz | 0.960740 | 1151.618528 | +--------------+-------------+--------------+ | 800 Hz | 0.952862 | 1449.801829 | +--------------+-------------+--------------+ | 1 kHz | 0.944302 | 1825.192365 | +--------------+-------------+--------------+ | 1.25 kHz | 0.934099 | 2297.781050 | +--------------+-------------+--------------+ | 1.6 kHz | 0.920614 | 2892.734954 | +--------------+-------------+--------------+ | 2 kHz | 0.901401 | 3641.737544 | +--------------+-------------+--------------+ | 2.5 kHz | 0.872970 | 4584.675937 | +--------------+-------------+--------------+ | 3.15 kHz | 0.830558 | 5771.765042 | +--------------+-------------+--------------+ | 4 kHz | 0.768147 | 7266.221682 | +--------------+-------------+--------------+ | 5 kHz | 0.679337 | 9147.631123 | +--------------+-------------+--------------+ | 6.3 kHz | 0.560055 | 11516.185278 | +--------------+-------------+--------------+ | 8 kHz | 0.413902 | 14498.018294 | +--------------+-------------+--------------+ | 10 kHz | 0.258501 | 18251.923651 | +--------------+-------------+--------------+ | 12.5 kHz | 0.125124 | 22977.810498 | +--------------+-------------+--------------+ | 16 kHz | 0.041573 | 28927.349543 | +--------------+-------------+--------------+ | In Code_TYMPAN : | OSpectre AtmosphericConditions::compute_length_absorption(double length) const, calcule le module Aatmos. | void TYChemin::calcAttenuation(const TYTabEtape& tabEtapes, const AtmosphericConditions& atmos), calcule la phase Aatmos