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Sound Pressure Level in Decibels (Root Mean Square Pressure) Formula

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Sound Level in Decibels (dB) is the logarithmic measure of the ratio of a particular sound pressure to a reference sound pressure. Check FAQs

L = 20 \cdot \log 10 (\frac{P m}{20 \cdot 10^{- 6}})

L - Sound Level in Decibels?P_m - Pressure RMS in Micropascal?

Sound Pressure Level in Decibels (Root Mean Square Pressure) Example

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Here is how the Sound Pressure Level in Decibels (Root Mean Square Pressure) equation looks like with Values.

Here is how the Sound Pressure Level in Decibels (Root Mean Square Pressure) equation looks like with Units.

Here is how the Sound Pressure Level in Decibels (Root Mean Square Pressure) equation looks like.

20 = 20 \cdot \log 10 (\frac{200}{20 \cdot 10^{- 6}})

20dB = 20 \cdot \log 10 (\frac{200μPa}{20 \cdot 10^{- 6}})

20 = 20 \cdot \log 10 (\frac{200}{20 \cdot 10^{- 6}})

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Sound Pressure Level in Decibels (Root Mean Square Pressure) Solution

Follow our step by step solution on how to calculate Sound Pressure Level in Decibels (Root Mean Square Pressure)?

FIRST Step Consider the formula

L = 20 \cdot \log 10 (\frac{P m}{20 \cdot 10^{- 6}})

Next Step Substitute values of Variables

∴

L = 20 \cdot \log 10 (\frac{200μPa}{20 \cdot 10^{- 6}})

Next Step Convert Units

∴

L = 20 \cdot \log 10 (\frac{0.0002Pa}{20 \cdot 10^{- 6}})

Next Step Prepare to Evaluate

∴

L = 20 \cdot \log 10 (\frac{0.0002}{20 \cdot 10^{- 6}})

LAST Step Evaluate

∴

L = 20dB

Sound Pressure Level in Decibels (Root Mean Square Pressure) Formula Elements

Variables

Functions

Sound Level in Decibels

Sound Level in Decibels (dB) is the logarithmic measure of the ratio of a particular sound pressure to a reference sound pressure.

Symbol: L

Measurement: SoundUnit: dB

Note: Value should be greater than 0.

Formulas to find Sound Level in Decibels

Pressure RMS in Micropascal

The Pressure RMS in Micropascal refers to the root mean square value, it is the local pressure deviation from the ambient atmospheric pressure, caused by a sound wave.

Symbol: P_m

Measurement: PressureUnit: μPa

Note: Value should be greater than 0.

Formulas to find Pressure RMS in Micropascal

log10

The common logarithm, also known as the base-10 logarithm or the decimal logarithm, is a mathematical function that is the inverse of the exponential function.

Syntax: log10(Number)

Other formulas in Sound Pressure category

Go Sound Pressure

P s = P atm - P b

Go Total Atmospheric Pressure given Sound Pressure

P atm = P s + P b

Go Barometric Pressure given Sound Pressure

P b = P atm - P s

How to Evaluate Sound Pressure Level in Decibels (Root Mean Square Pressure)?

Sound Pressure Level in Decibels (Root Mean Square Pressure) evaluator uses Sound Level in Decibels = 20*log10(Pressure RMS in Micropascal/(20*10^(-6))) to evaluate the Sound Level in Decibels, The Sound Pressure Level in Decibels (Root Mean Square Pressure) Pressure formula is defined as the pressure level of a sound, measured in decibels (dB). Sound Level in Decibels is denoted by L symbol.

How to evaluate Sound Pressure Level in Decibels (Root Mean Square Pressure) using this online evaluator? To use this online evaluator for Sound Pressure Level in Decibels (Root Mean Square Pressure), enter Pressure RMS in Micropascal (P_m) and hit the calculate button.

FAQs on Sound Pressure Level in Decibels (Root Mean Square Pressure)

What is the formula to find Sound Pressure Level in Decibels (Root Mean Square Pressure)?

The formula of Sound Pressure Level in Decibels (Root Mean Square Pressure) is expressed as Sound Level in Decibels = 20*log10(Pressure RMS in Micropascal/(20*10^(-6))). Here is an example- 25.10545 = 20*log10(0.0002/(20*10^(-6))).

How to calculate Sound Pressure Level in Decibels (Root Mean Square Pressure)?

With Pressure RMS in Micropascal (P_m) we can find Sound Pressure Level in Decibels (Root Mean Square Pressure) using the formula - Sound Level in Decibels = 20*log10(Pressure RMS in Micropascal/(20*10^(-6))). This formula also uses Common Logarithm (log10) function(s).

Can the Sound Pressure Level in Decibels (Root Mean Square Pressure) be negative?

No, the Sound Pressure Level in Decibels (Root Mean Square Pressure), measured in Sound cannot be negative.

Which unit is used to measure Sound Pressure Level in Decibels (Root Mean Square Pressure)?

Sound Pressure Level in Decibels (Root Mean Square Pressure) is usually measured using the Decibel[dB] for Sound. Bel[dB], Neper[dB] are the few other units in which Sound Pressure Level in Decibels (Root Mean Square Pressure) can be measured.

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