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

>Model

ID:(1588, 0)

Iframe

>Top

ID:(15459, 0)

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Parameters

$I_{ref}$

I_ref

Reference intensity, air

W/m^2

$p_{ref}$

p_ref

Reference pressure

Pa

$P$

P

Sound Power

W

Variables

$e$

e

Energy density

J/m^3

$\rho$

rho

Mean density

kg/m^3

$u$

u

Molecule speed

m/s

$L$

L

Noise level, air

dB

$S$

S

Section of Volume DV

m^2

$I$

I

Sound Intensity

W/m^2

$p$

p

Sound pressure

Pa

$c$

c

Speed of sound

m/s

Calculations

• Alternative method
• Traditional method
• Strategy
• 2D
• 3D

Equation

Number

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

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Calculations

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable Given Calculate Target : Equation To be used

Equations

ID:(15454, 0)

Equation

>Top, >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:

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

Conditions

Variables

$S$

Section of Volume DV

$m^2$

5081

$I$

Sound Intensity

$W/m^2$

5091

$W$

Sound Power

$W$

5090

Relation

ID:(3193, 0)

Equation

>Top, >Model

Si se toma la energía E por oscilación se puede escribir la potencia en función de la energía y el periodo T se tiene que

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

Si por otro lado con la variación del volumen es

y con section of Volume DV $m^2$, sound Intensity $W/m^2$ and sound Power $W$ la intensidad sonora es

por lo que

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

osea con section of Volume DV $m^2$, sound Intensity $W/m^2$ and sound Power $W$ es

$I = c e$

Conditions

Variables

$e$

Energy density

$J/m^3$

4932

$I$

Sound Intensity

$W/m^2$

5091

$c$

Speed of sound

$m/s$

5073

Relation

ID:(3406, 0)

Equation

>Top, >Model

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

$e =\displaystyle\frac{1}{2} \rho u ^2$

Conditions

Variables

$e$

Energy density

$J/m^3$

4932

$\rho$

Mean density

$kg/m^3$

5088

$u$

Molecule speed

$m/s$

5072

Relation

Development

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:

$e =\displaystyle\frac{1}{2} \rho u ^2$

ID:(3400, 0)

Equation

>Top, >Model

Como la densidad de la energía cinética es con energy density $J/m^3$, mean density $kg/m^3$ and molecule speed $m/s$

se tiene que con energy density $J/m^3$, sound Intensity $W/m^2$ and speed of sound $m/s$

que la intensidad es con energy density $J/m^3$, sound Intensity $W/m^2$ and speed of sound $m/s$

$I =\displaystyle\frac{1}{2} \rho c u ^2$

Conditions

Variables

$\rho$

Mean density

$kg/m^3$

5088

$u$

Molecule speed

$m/s$

5072

$I$

Sound Intensity

$W/m^2$

5091

$c$

Speed of sound

$m/s$

5073

Relation

ID:(3404, 0)

Equation

>Top, >Model

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

$I =\displaystyle\frac{ p ^2}{2 \rho c }$

Conditions

Variables

$\rho$

Mean density

$kg/m^3$

5088

$I$

Sound Intensity

$W/m^2$

5091

$p$

Sound pressure

$Pa$

5084

$c$

Speed of sound

$m/s$

5073

Relation

Development

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

$I =\displaystyle\frac{1}{2} \rho c u ^2$

and since the sound pressure ($p$) is defined as

$p = \rho c u$

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

$I =\displaystyle\frac{ p ^2}{2 \rho c }$

ID:(3405, 0)

Equation

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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, air ($L$) is indicated not in the sound Intensity ($I$) or the reference intensity, air ($I_{ref}$), but in the base ten logarithm of these magnitudes. Particularly, we take the lowest sound intensity we can perceive, the reference intensity, air ($I_{ref}$)

, and use it as a reference. The new scale is defined with as follows:

$L = 10 log_{10}\left(\displaystyle\frac{ I }{ I_{ref} }\right)$

Conditions

Variables

$L$

Noise level, air

$dB$

5119

$I_{ref}$

Reference intensity, air

20e-6

$W/m^2$

5120

$I$

Sound Intensity

$W/m^2$

5091

Relation

ID:(3194, 0)

Equation

>Top, >Model

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 ($p$), the mean density ($\rho$), and the speed of sound ($c$), and is equal to

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

$I_{ref} =\displaystyle\frac{ p_{ref} ^2}{2 \rho c }$

Conditions

Variables

$\rho$

Mean density

$kg/m^3$

5088

$I_{ref}$

Reference intensity, air

20e-6

$W/m^2$

5120

$p_{ref}$

Reference pressure

3.65e+10

$Pa$

5121

$c$

Speed of sound

$m/s$

5073

Relation

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, 0)