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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.

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ID:(1588, 0)



Sound Intensity

Storyboard

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

Variables

Symbol
Text
Variable
Value
Units
Calculate
MKS Value
MKS Units
e
e
Energy density
J/m^3
\rho
rho
Mean density
kg/m^3
u
u
Molecule speed
m/s
L
L
Noise level
dB
I_{ref}
I_ref
Reference intensity
W/m^2
p_{ref}
p_ref
Reference pressure
Pa
S
S
Section of Volume DV
m^2
I
I
Sound Intensity
W/m^2
P
P
Sound Power
W
p_s
p_s
Sound pressure
Pa
c
c
Speed of sound
m/s

Calculations


First, select the equation:   to ,  then, select the variable:   to 

Symbol
Equation
Solved
Translated

Calculations

Symbol
Equation
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Translated

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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:

equation

The sound Intensity (I) can be calculated from the mean density (\rho), the molecule speed (u), and the molar concentration (c) using

equation=3404

and since the sound pressure (p_s) is defined as

equation=3391

it follows that the sound Intensity (I) can be expressed in terms of the sound pressure (p_s) by

equation


Examples


mechanisms


model

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:

kyon

Si se toma la energ a E por oscilaci n se puede escribir la potencia en funci n de la energ a y el periodo T se tiene que

W=\displaystyle\frac{E}{T}



Si por otro lado con list=3398 la variaci n del volumen es

equation=3398



y con list=3193 la intensidad sonora es

equation=3193

por lo que

I=\displaystyle\frac{W}{S}=\displaystyle\frac{E}{ST}=\displaystyle\frac{cE}{ScT}=\displaystyle\frac{cE}{V}



osea con list es

kyon

The the energy density (e) is obtained from the mean density (\rho) and the molecule speed (u) as follows:

kyon

Como la densidad de la energ a cin tica es con list=3400

equation=3400



se tiene que con list=3406

equation=3406



que la intensidad es con list

kyon

The sound Intensity (I) can be calculated from the mean density (\rho), the sound pressure (p_s) The molar concentration (c) with

kyon

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 list as follows:

kyon

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

equation=3405

we can calculate a value for the reference intensity (I_{ref}) based on the value of the reference pressure, water (p_{ref}):

kyon

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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