Intensity (physics)

Intensity
Intensity
Dimension	MT −3
Units
SI	W / m²
GHS	erg / scm²
Notes
	scalar value

Intensity is a scalar physical quantity that quantitatively characterizes the power carried by a wave in the direction of propagation. Numerically, the intensity is equal to the radiation power averaged over a period of wave oscillations passing through a unit area located perpendicular to the direction of energy propagation. In mathematical form, this can be expressed as follows:

I(t)={\frac {1}{T}}\int \limits _{t}^{t+T}{\frac {dP}{dS}}dt,

{\ displaystyle I (t) = {\ frac {1} {T}} \ int \ limits _ {t} ^ {t + T} {\ frac {dP} {dS}} dt,}

I (t) = {\ frac {1} {T}} \ int \ limits _ {t} ^ {{t + T}} {\ frac {dP} {dS}} dt,

Where $T$ ${\ displaystyle T}$ $T$ - period of the wave, $d P$ ${\ displaystyle dP}$ $dP$ - power carried by the wave through the site $d S$ ${\ displaystyle dS}$ $dS$ .

The wave intensity is related to the average energy density $W$ ${\ displaystyle W}$ $W$ in wave and wave propagation velocity $v$ ${\ displaystyle v}$ $v$ the following relation:

I=Wv.

{\ displaystyle I = Wv.}

I = Wv.

The unit of intensity in the International System of Units (SI) is W / m², in the GHS system - erg / s · cm².

Intensity of electromagnetic radiation

Electromagnetic radiation (for example, light ) is a set of waves , the oscillations in which make the electric field and magnetic induction . Electromagnetic waves carry the energy of an electromagnetic field , the flux of which is determined by the value of the Poynting vector. The intensity of electromagnetic radiation is equal to the average value of the Poynting vector modulus ^[1] :

I(t)={\frac {1}{T}}\int \limits _{t}^{t+T}\left|{\vec {S}}(t)\right|dt,

{\ displaystyle I (t) = {\ frac {1} {T}} \ int \ limits _ {t} ^ {t + T} \ left | {\ vec {S}} (t) \ right | dt, }

I(t)={\frac {1}{T}}\int \limits _{t}^{{t+T}}\left|{\vec S}(t)\right|dt,

where is the Poynting vector ${\vec {S}}(t)={\frac {c}{4\pi }}\left[{\vec {E}}(t)\times {\vec {B}}(t)\right],$ ${\ displaystyle {\ vec {S}} (t) = {\ frac {c} {4 \ pi}} \ left [{\ vec {E}} (t) \ times {\ vec {B}} (t ) \ right],}$ ${\vec S}(t)={\frac {c}{4\pi }}\left[{\vec E}(t)\times {\vec B}(t)\right],$ (in the GHS system), $E$ ${\ displaystyle E}$ $E$ Is the electric field strength, and $B$ ${\ displaystyle B}$ $B$ - magnetic induction.

For a monochromatic linearly polarized wave with an amplitude of the electric field $E_{0}$ ${\ displaystyle E_ {0}}$ $E_{0}$ intensity is equal to:

I={\frac {cE_{0}^{2}}{8\pi }}.

{\ displaystyle I = {\ frac {cE_ {0} ^ {2}} {8 \ pi}}.}

I={\frac {cE_{0}^{2}}{8\pi }}.

For a monochromatic circularly polarized wave, this value is twice as large:

I={\frac {cE_{0}^{2}}{4\pi }}.

{\ displaystyle I = {\ frac {cE_ {0} ^ {2}} {4 \ pi}}.}

Sound Intensity

Sound is a wave of mechanical vibrations of the medium. Sound intensity can be expressed in terms of the amplitude values of sound pressure p and vibrational velocity of the medium v :

I={\frac {pv}{2}}.

{\ displaystyle I = {\ frac {pv} {2}}.}

Notes

↑ Here and below in the section, the Gaussian system of units is used

[1] Here and below in the section, the Gaussian system of units is used

Intensity
$I$ ${\ displaystyle I}$ $I$
Dimension	MT ⁻³
Units
SI	W / m²
GHS	erg / scm²
Notes
scalar value

Intensity (physics)

Intensity of electromagnetic radiation

Sound Intensity

Notes

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