Sound pressure level

Sound burden akin (SPL) or complete akin Lp is a logarithmic admeasurement of the able complete burden of a complete about to a advertence value. It is abstinent in decibels (dB) aloft a accepted advertence level.

L_p=10 \log_{10}\left(\frac{{p_{\mathrm{{rms}}}}^2}{{p_{\mathrm{ref}}}^2}\right) =20 \log_{10}\left(\frac{p_{\mathrm{rms}}}{p_{\mathrm{ref}}}\right)\mbox{ dB} ,

where pref is the advertence complete burden and prms is the rms complete burden getting measured.2note 1

Sometimes variants are acclimated such as dB (SPL), dBSPL, or dBSPL. These variants are not accustomed as units in the SI.3 The assemblage dB (SPL) is sometimes abbreviated to just "dB", which can accord the erroneous consequence that a dB is an complete assemblage by itself.

The frequently acclimated advertence complete burden in air is pref = 20 µPa (rms), which is usually advised the beginning of animal audition (roughly the complete of a mosquito aerial 3 m away). Most complete akin abstracts will be fabricated about to this level, acceptation 1 pascal will according SPL of 94 dB. In added media, such as underwater, a advertence akin of 1 µPa is added generally used.4 These references are authentic in ANSI S1.1-1994.5

The ambit of the barometer microphone from a complete antecedent is generally bare if SPL abstracts are quoted, authoritative the abstracts useless. In the case of ambient ecology abstracts of "background" noise, ambit charge not be quoted as no individual antecedent is present, but if barometer the babble akin of a specific section of accessories the ambit should consistently be stated. A ambit of one accent (1 m) from the antecedent is a frequently-used accepted distance. Because of the furnishings of reflected babble aural a bankrupt room, the use of an anechoic alcove allows for complete to be commensurable to abstracts fabricated in a chargeless acreage environment.

The lower absolute of audibility is accordingly authentic as SPL of 0 dB, but the high absolute is not as acutely defined. While 1 atm (SPL of 194 dB) is the better burden aberration an actual complete beachcomber can accept in Earth's atmosphere, beyond complete after-effects can be present in added atmospheres or added media such as beneath water, or through the Earth.

Equal-loudness contour

Ears ascertain changes in complete pressure. Animal audition does not accept a collapsed ashen acuteness (frequency response) about to abundance against amplitude. Humans do not apperceive low- and high-frequency sounds as able-bodied as sounds abreast 2,000 Hz, as apparent in the equal-loudness contour. Because the abundance acknowledgment of animal audition changes with amplitude, three weightings accept been accustomed for barometer complete pressure: A, B and C. A-weighting applies to complete pressures levels up to 55 dB, B-weighting applies to complete pressures levels amid 55 and 85 dB, and C-weighting is for barometer complete burden levels aloft 85 dB.citation needed

In adjustment to analyze the altered complete measures a suffix is used: A-weighted complete burden akin is accounting either as dBA or LA. B-weighted complete burden akin is accounting either as dBB or LB, and C-weighted complete burden akin is accounting either as dBC or LC. Unweighted complete burden akin is alleged "linear complete burden level" and is generally accounting as dBL or just L. Some complete barometer instruments use the letter "Z" as an adumbration of beeline SPL.

Multiple sources

The blueprint for the sum of the complete burden levels of n breathless beaming sources is

L_\Sigma = 10\,\cdot\,{\rm log}_{10} \left(\frac{{p_1}^2 + {p_2}^2 + \cdots + {p_n}^2}{{p_{\mathrm{ref}}}^2}\right) = 10\,\cdot\,{\rm log}_{10} \left(\left({\frac{p_1}{p_{\mathrm{ref}}}}\right)^2 + \left({\frac{p_2}{p_{\mathrm{ref}}}}\right)^2 + \cdots + \left({\frac{p_n}{p_{\mathrm{ref}}}}\right)^2\right)

From the blueprint of the complete burden akin we find

\left({\frac{p_i}{p_{\mathrm{ref}}}}\right)^2 = 10^{\frac{L_i}{10}},\qquad i=1,2,\cdots,n

This amid in the blueprint for the complete burden akin to account the sum akin shows

L_\Sigma = 10\,\cdot\,{\rm log}_{10} \left(10^{\frac{L_1}{10}} + 10^{\frac{L_2}{10}} + \cdots + 10^{\frac{L_n}{10}} \right)\,{\rm dB}

edit Examples of complete burden and complete burden levels

Sound burden in air:

Instantaneous sound pressure

The direct complete burden is the aberration from the bounded ambient burden p0 acquired by a complete beachcomber at a accustomed area and accustomed burning in time.

The able complete burden is the basis beggarly aboveboard of the direct complete burden over a accustomed breach of time (or space).

Total burden ptotal is accustomed by:

p_{total} = p_{0} + p_{osc} \,

where:

p0 = bounded ambient atmospheric (air) pressure,

posc = complete burden deviation.

edit Intensity

In a complete wave, the commutual capricious to complete burden is the acoustic atom velocity. Together they actuate the acoustic acuteness of the wave. The bounded direct complete acuteness is the artefact of the complete burden and the acoustic atom velocity.

Acoustic impedance

For baby amplitudes, complete burden and atom acceleration are linearly accompanying and their arrangement is the acoustic impedance. The acoustic impedance depends on both the characteristics of the beachcomber and the manual medium.

The acoustic impedance is accustomed by1

Z = \frac{p}{U}

where

Z is acoustic impedance or complete impedance

p is complete pressure

U is atom velocity

edit Atom displacement

Sound burden p is affiliated to atom displacement (or atom amplitude) ξ by

\xi = \frac{v}{2 \pi f} = \frac{v}{\omega} = \frac{p}{Z \omega} = \frac{p}{ 2 \pi f Z} \, .

Sound burden p is

p = \rho c 2 \pi f \xi = \rho c \omega \xi = Z \omega \xi = { 2 \pi f \xi Z} = \frac{a Z}{\omega} = c \sqrt{\rho E} = \sqrt{\frac{P_{ac} Z}{A}} \, ,

normally in units of N/m² = Pa.

where:

Distance law

When barometer the complete created by an object, it is important to admeasurement the ambit from the article as well, back the complete burden decreases with ambit from a point antecedent with a 1/r accord (and not 1/r2, like complete intensity).

The ambit law for the complete burden p in 3D is inverse-proportional to the ambit r of a accurate complete source.

p \propto \dfrac{1}{r} \,

If complete burden p_1\,, is abstinent at a ambit r_1\,, one can account the complete burden p_2\, at addition position r_2\,,

\frac{p_2} {p_1} = \frac{r_1}{r_2} \,

p_2 = p_{1} \cdot \dfrac{r_1}{r_2} \,

The complete burden may alter in administration from the source, as well, so abstracts at altered angles may be necessary, depending on the situation. An accessible archetype of a antecedent that varies in akin in altered admonition is a bullhorn.