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Sound Propagation
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The sound wave is propagated so that its energy per area element is reduced as it moves away from the source.

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ID:(386, 0)


Propagation of Sound
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Sound propagates and interacts with various edges and objects. On flat surfaces it is reflected under the same angle it affects (ground, building). However, the wind leads to refraction with what the beams bend:

ID:(516, 0)


Spherical propagation
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For a point source, the sound spreads in all directions uniformly. Therefore, the sound level will be reduced due to the effect that the energy is distributed over a surface of a sphere of radius r equal to the path traveled

ID:(11829, 0)


Propagation of the intensity
Equation

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Si consideramos una fuente puntual, la intensidad del sonido es con

$ I =\displaystyle\frac{ P }{ S }$



se propagara en forma esférica. En este caso la superficie es con

$ S = 4 \pi r ^2$



con lo que la intensidad es con

$ I =\displaystyle\frac{1}{4 \pi }\displaystyle\frac{ W }{ r ^2}$

$r$
Distance between Emitter and Receiver
$m$
$I$
Intensity in the distance
$W/m^2$
$\pi$
Pi
3.1415927
$rad$
$W$
Sound Power
$W$

ID:(3402, 0)


Propagation depending on the Intensity at source
Equation

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Si se considera una esfera en torno de la fuente a un radio r_0 la potencia W sera igual a\\n\\n

$W=4\pi r_0^2 I_0$



por lo que la intensidad es con distance between Emitter and Receiver $m$, intensity in the distance $W/m^2$, pi $rad$ and sound Power $W$

$ I =\displaystyle\frac{1}{4 \pi }\displaystyle\frac{ W }{ r ^2}$



a una distancia r tendrá con distance between Emitter and Receiver $m$, intensity in the distance $W/m^2$, pi $rad$ and sound Power $W$ la magnitud:

$ I =\displaystyle\frac{ r_0 ^2}{ r ^2} I_0 $

$r$
Distance between Emitter and Receiver
$m$
$I$
Intensity in the distance
$W/m^2$
$I_0$
Intensity on the Surface of the Source
$W/m^2$
$r_0$
Source Size
$m$

ID:(3403, 0)


Sum of intensities and powers
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Since the different beams do not interact, the intensity and power that occurs at any point in space is equal to the sum of the individual contributions:

ID:(11830, 0)


Sum of intensities
Equation

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Como los distintos haces no interactuan la intensidad que se da en cualquier punto del espacio es igual a la suma de las contribuciones individuales.

Con la intensidad total es

$ I = \displaystyle\sum_i I_i $

$I_i$
Intensidad Sonora de la fuente i
$W/m^2$
$I_{tot}$
Total Loudness
$W/m^2$

ID:(11831, 0)


Sum of powers
Equation

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Como los distintos haces no interactuan la potencia que se da en cualquier punto del espacio es igual a la suma de las contribuciones individuales.

Con la potencia total es

$ W = \displaystyle\sum_i W_i $

$W_i$
Potencia Sonora de la fuente i
$W$
$W_{tot}$
Total sound power
$W$

ID:(11832, 0)


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Video

Video: Sound propagation