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Sound propagation
Storyboard 
The sound wave is propagated so that its energy per area element is reduced as it moves away from the source.
ID:(386, 0)
Propagation depending on the Intensity at source
Definition
Si se considera una esfera en torno de la fuente a un radio
$W=4\pi r_0^2 I_0$
por lo que la intensidad es con distance between Emitter and Receiver $m$, intensity in the distance $W/m^2$ and sound Power $W$
| $ I =\displaystyle\frac{1}{4 \pi }\displaystyle\frac{ P }{ r ^2}$ |
a una distancia
| $ I =\displaystyle\frac{ r_0 ^2}{ r ^2} I_0 $ |
ID:(15567, 0)
Propagation of the intensity
Image
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{ P }{ r ^2}$ |
ID:(15566, 0)
Propagation of Sound
Note
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
Quote
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
ID:(11829, 0)
Sum of intensities and powers
Exercise
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)
Sound propagation
Description
The sound wave is propagated so that its energy per area element is reduced as it moves away from the source.
Variables
Calculations
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then, select the variable: 
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Calculations
Variable
Given
Calculate
Target :
Equation
To be used
Equations
Examples
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)
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
(ID 11829)
Si consideramos una fuente puntual, la intensidad del sonido es con
| $ I =\displaystyle\frac{ P }{ S }$ |
se propagara en forma esf rica. 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{ P }{ r ^2}$ |
(ID 15566)
Si se considera una esfera en torno de la fuente a un radio
$W=4\pi r_0^2 I_0$
por lo que la intensidad es con distance between Emitter and Receiver $m$, intensity in the distance $W/m^2$ and sound Power $W$
| $ I =\displaystyle\frac{1}{4 \pi }\displaystyle\frac{ P }{ r ^2}$ |
a una distancia
| $ I =\displaystyle\frac{ r_0 ^2}{ r ^2} I_0 $ |
(ID 15567)
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)
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 $ |
(ID 11831)
(ID 15455)
Si consideramos una fuente puntual, la intensidad del sonido es con
| $ I =\displaystyle\frac{ P }{ S }$ |
se propagara en forma esf rica. 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{ P }{ r ^2}$ |
(ID 3402)
Si se considera una esfera en torno de la fuente a un radio
$W=4\pi r_0^2 I_0$
por lo que la intensidad es con distance between Emitter and Receiver $m$, intensity in the distance $W/m^2$ and sound Power $W$
| $ I =\displaystyle\frac{1}{4 \pi }\displaystyle\frac{ P }{ r ^2}$ |
a una distancia
| $ I =\displaystyle\frac{ r_0 ^2}{ r ^2} I_0 $ |
(ID 3403)
Just like in other human sensory systems, our hearing is capable of detecting pressure variations over a wide range $(10^{-5}-10^2 Pa)$. However, when we perceive a signal doubling, it doesn't correspond to double the pressure or sound intensity, but rather the square of these magnitudes. In other words, our signal detection capacity operates on a logarithmic and nonlinear scale.
Hence, the noise level ($L$) is indicated not in the sound Intensity ($I$) or the reference intensity ($I_{ref}$), but in the base ten logarithm of these magnitudes. Particularly, we take the lowest sound intensity we can perceive, the reference intensity ($I_{ref}$)
, and use it as a reference. The new scale is defined with as follows:
| $ L = 10 log_{10}\left(\displaystyle\frac{ I }{ I_{ref} }\right)$ |
(ID 3194)
The sound pressure level that we can detect with our ear, denoted as the reference pressure, water ($p_{ref}$), is $2 \times 10^{-5} , Pa$.
Since the sound Intensity ($I$) is associated with the sound pressure ($p_s$), the mean density ($\rho$), and the speed of sound ($c$), and is equal to
| $ I =\displaystyle\frac{ p ^2}{2 \rho c }$ |
we can calculate a value for the reference intensity ($I_{ref}$) based on the value of the reference pressure, water ($p_{ref}$):
| $ I_{ref} =\displaystyle\frac{ p_{ref} ^2}{2 \rho c }$ |
This is achieved with a density of $1.27 , kg/m^3$ and a sound speed of $331 , m/s$, equivalent to $9.5 \times 10^{-13} , W/m^2$.
(ID 3409)
The noise level ($L$) encompasses a wide range of the sound pressure ($p_s$), making it useful to define a scale that mitigates this difficulty. To do so, we can work with the logarithm of the pressure normalized by a value corresponding to zero on this scale. If we take the minimum pressure that a person can detect, defined as the reference pressure ($p_{ref}$), we can define a scale using:
| $ L = 20 \log_{10}\left(\displaystyle\frac{ p_s }{ p_{ref} }\right)$ |
which starts at 0 for the audible range. In the case of air, the reference pressure ($p_{ref}$) is $20 \mu Pa$.
(ID 3407)
ID:(386, 0)