
Sound Intensity
Storyboard 
Sound intensity is the energy by area and time that helps to understand how the sound wave is distributed spatially.
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Sound Intensity
Storyboard 
Sound intensity is the energy by area and time that helps to understand how the sound wave is distributed spatially.

Variables

Calculations




Calculations







Equations
The energy that a sound wave contributes to the medium in which sound propagates corresponds to the kinetic energy of the particles. With the molecule speed (u) and the mass of a volume of the medium (m) The wave energy (E), it equals the kinetic energy:
E=\displaystyle\frac{1}{2}mu^2
the energy density (e) is obtained by dividing the wave energy (E) by the volume with molecules (\Delta V), giving:
e=\displaystyle\frac{E}{\Delta V}
Introducing the mean density (\rho) as:
\rho=\displaystyle\frac{m}{\Delta V}
yields the energy density:
The sound Intensity (I) can be calculated from the mean density (\rho), the molecule speed (u), and the molar concentration (c) using
and since the sound pressure (p_s) is defined as
it follows that the sound Intensity (I) can be expressed in terms of the sound pressure (p_s) by

Examples
Intensity is the power (energy per unit time, in joules per second or watts) per area emanating from a source.
Therefore, it is defined as the sound Intensity (I), the ratio between the sound Power (P) and the section of Volume DV (S), so it is:
Si se toma la energ a
W=\displaystyle\frac{E}{T}
Si por otro lado con
y con
por lo que
I=\displaystyle\frac{W}{S}=\displaystyle\frac{E}{ST}=\displaystyle\frac{cE}{ScT}=\displaystyle\frac{cE}{V}
osea con
The the energy density (e) is obtained from the mean density (\rho) and the molecule speed (u) as follows:
Como la densidad de la energ a cin tica es con
se tiene que con
que la intensidad es con
The sound Intensity (I) can be calculated from the mean density (\rho), the sound pressure (p_s) The molar concentration (c) with
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
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
we can calculate a value for the reference intensity (I_{ref}) based on the value of the reference pressure, water (p_{ref}):
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.
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