✖Sound Intensity Level is the logarithmic measure of the sound power per unit area, expressed in decibels (dB).ⓘ Sound Intensity Level [I]			+10% -10%
✖The density of air is the mass per unit volume of Earth's atmosphere, typically around 1.225 kg/m³ at sea level and 15°C, affecting sound propagation and weather.ⓘ Density of Air [ρ]			+10% -10%
✖The Velocity of sound wave is the speed of sound with the distance traveled per unit of time by a sound wave.ⓘ Velocity of sound wave [C]			+10% -10%

✖Pressure RMS is the root mean square value is the local pressure deviation from the ambient atmospheric pressure, caused by a sound wave.ⓘ Root Mean Square Pressure given Sound Intensity [P_rms]

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Formula

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Root Mean Square Pressure given Sound Intensity

Formula

`"P"_{"rms"} = sqrt("I"*"ρ"*"C")`

Example

`"0.000211Pa"=sqrt("1E^-10W/m²"*"1.293kg/m³"*"343m/s")`

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Root Mean Square Pressure given Sound Intensity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure RMS = sqrt(Sound Intensity Level*Density of Air*Velocity of sound wave)
P_rms = sqrt(I*ρ*C)
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Pressure RMS - (Measured in Pascal) - Pressure RMS is the root mean square value is the local pressure deviation from the ambient atmospheric pressure, caused by a sound wave.
Sound Intensity Level - (Measured in Watt per Square Meter) - Sound Intensity Level is the logarithmic measure of the sound power per unit area, expressed in decibels (dB).
Density of Air - (Measured in Kilogram per Cubic Meter) - The density of air is the mass per unit volume of Earth's atmosphere, typically around 1.225 kg/m³ at sea level and 15°C, affecting sound propagation and weather.
Velocity of sound wave - (Measured in Meter per Second) - The Velocity of sound wave is the speed of sound with the distance traveled per unit of time by a sound wave.

STEP 1: Convert Input(s) to Base Unit

Sound Intensity Level: 1E-10 Watt per Square Meter --> 1E-10 Watt per Square Meter No Conversion Required
Density of Air: 1.293 Kilogram per Cubic Meter --> 1.293 Kilogram per Cubic Meter No Conversion Required
Velocity of sound wave: 343 Meter per Second --> 343 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_rms = sqrt(I*ρ*C) --> sqrt(1E-10*1.293*343)

Evaluating ... ...

P_rms = 0.000210594159463172

STEP 3: Convert Result to Output's Unit

0.000210594159463172 Pascal --> No Conversion Required

FINAL ANSWER

0.000210594159463172 ≈ 0.000211 Pascal <-- Pressure RMS

(Calculation completed in 00.006 seconds)

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Created by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 2 Root Mean Square Pressure Calculators

Root Mean Square Pressure given Sound Intensity

Go Pressure RMS = sqrt(Sound Intensity Level*Density of Air*Velocity of sound wave)

Root Mean Square Pressure when Sound Pressure Level

Go Pressure RMS in Micropascal = (20*10^(-6))*10^(Sound Level in Decibels/20)

Root Mean Square Pressure given Sound Intensity Formula

Pressure RMS = sqrt(Sound Intensity Level*Density of Air*Velocity of sound wave)
P_rms = sqrt(I*ρ*C)

What is sound intensity?

Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.

How to Calculate Root Mean Square Pressure given Sound Intensity?

Root Mean Square Pressure given Sound Intensity calculator uses Pressure RMS = sqrt(Sound Intensity Level*Density of Air*Velocity of sound wave) to calculate the Pressure RMS, Root Mean Square Pressure given Sound Intensity is square root of average of square of pressure of sound signal over given duration. Pressure RMS is denoted by P_rms symbol.

How to calculate Root Mean Square Pressure given Sound Intensity using this online calculator? To use this online calculator for Root Mean Square Pressure given Sound Intensity, enter Sound Intensity Level (I), Density of Air (ρ) & Velocity of sound wave (C) and hit the calculate button. Here is how the Root Mean Square Pressure given Sound Intensity calculation can be explained with given input values -> 0.000211 = sqrt(1E-10*1.293*343).

FAQ

What is Root Mean Square Pressure given Sound Intensity?

Root Mean Square Pressure given Sound Intensity is square root of average of square of pressure of sound signal over given duration and is represented as P_rms = sqrt(I*ρ*C) or Pressure RMS = sqrt(Sound Intensity Level*Density of Air*Velocity of sound wave). Sound Intensity Level is the logarithmic measure of the sound power per unit area, expressed in decibels (dB), The density of air is the mass per unit volume of Earth's atmosphere, typically around 1.225 kg/m³ at sea level and 15°C, affecting sound propagation and weather & The Velocity of sound wave is the speed of sound with the distance traveled per unit of time by a sound wave.

How to calculate Root Mean Square Pressure given Sound Intensity?

Root Mean Square Pressure given Sound Intensity is square root of average of square of pressure of sound signal over given duration is calculated using Pressure RMS = sqrt(Sound Intensity Level*Density of Air*Velocity of sound wave). To calculate Root Mean Square Pressure given Sound Intensity, you need Sound Intensity Level (I), Density of Air (ρ) & Velocity of sound wave (C). With our tool, you need to enter the respective value for Sound Intensity Level, Density of Air & Velocity of sound wave and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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