Loudness Calculator

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✖Sound Intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.ⓘ Sound Intensity [I_s]			+10% -10%
✖Reference Intensity is the lowest intensity of sound a person with normal hearing can perceive.ⓘ Reference Intensity [I_ref]			+10% -10%

✖Loudness is the subjective perception of sound pressure. More formally, it is defined as, "That attribute of auditory sensation .ⓘ Loudness [Q]

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Formula

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Loudness

Formula

`"Q" = 10*log10("I"_{"s"}/"I"_{"ref"})`

Example

`"48.75061dB"=10*log10("75W/m²"/"0.001W/m²")`

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Loudness Solution

STEP 0: Pre-Calculation Summary

Formula Used

Loudness = 10*log10(Sound Intensity/Reference Intensity)
Q = 10*log10(I_s/I_ref)
This formula uses 1 Functions, 3 Variables

Functions Used

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., log10(Number)

Variables Used

Loudness - (Measured in Decibel) - Loudness is the subjective perception of sound pressure. More formally, it is defined as, "That attribute of auditory sensation .
Sound Intensity - (Measured in Watt per Square Meter) - Sound Intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.
Reference Intensity - (Measured in Watt per Square Meter) - Reference Intensity is the lowest intensity of sound a person with normal hearing can perceive.

STEP 1: Convert Input(s) to Base Unit

Sound Intensity: 75 Watt per Square Meter --> 75 Watt per Square Meter No Conversion Required
Reference Intensity: 0.001 Watt per Square Meter --> 0.001 Watt per Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q = 10*log10(I_s/I_ref) --> 10*log10(75/0.001)

Evaluating ... ...

Q = 48.750612633917

STEP 3: Convert Result to Output's Unit

48.750612633917 Decibel --> No Conversion Required

FINAL ANSWER

48.750612633917 ≈ 48.75061 Decibel <-- Loudness

(Calculation completed in 00.004 seconds)

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Created by Anirudh Singh

National Institute of Technology (NIT), Jamshedpur

Anirudh Singh has created this Calculator and 300+ more calculators!

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< 16 Waves And Sound Calculators

Length of Open Organ Pipe

Go Length of Organ Pipe = Number of Nodes/2*Velocity of Wave/Wave Frequency

Loudness

Go Loudness = 10*log10(Sound Intensity/Reference Intensity)

Velocity of Sound in Liquid

Go Velocity of Wave = sqrt(Bulk Modulus/Density)

Velocity of Sound in Solids

Go Velocity of Wave = sqrt(Elasticity/Density)

Mass per Unit Length of String

Go Mass per Unit Length = Tension of String/(Velocity of Wave^2)

Time Period given Velocity

Go Time Period of Progressive Wave = Wavelength/Velocity of Wave

Time Period using Angular Frequency

Go Time Period of Progressive Wave = (2*pi)/Angular Frequency

Tension in String

Go Tension of String = Velocity of Wave^2*Mass per Unit Length

Length of Closed Organ Pipe

Go Length of Organ Pipe = (2*Number of Nodes+1)*Wavelength/4

Wave Number using Angular Frequency

Go Wave Number = Angular Frequency/Velocity of Wave

Frequency of Wavelength using Velocity

Go Wave Frequency = Velocity of Wave/Wavelength

Frequency of Progressive Wave

Go Wave Frequency = Angular Frequency/(2*pi)

Intensity of Sound

Go Sound Intensity = Power/Normal Area

Wave Number

Go Wave Number = (2*pi)/Wavelength

Frequency of Wave using Time Period

Go Wave Frequency = 1/Time Period of Progressive Wave

Time Period using Frequency

Go Time Period of Progressive Wave = 1/Wave Frequency

Loudness Formula

Loudness = 10*log10(Sound Intensity/Reference Intensity)
Q = 10*log10(I_s/I_ref)

What is intensity of sound?

Intensity Of Sound is the quality or state of being intense especially , extreme degree of strength , force , energy or feeling . It is a magnitude of quantity per unit area.

How to Calculate Loudness?

Loudness calculator uses Loudness = 10*log10(Sound Intensity/Reference Intensity) to calculate the Loudness, Loudness refers to how loud or soft a sound seems to a listener. The loudness of sound is determined, in turn, by the intensity of the sound waves. Intensity is a measure of the amount of energy in sound waves. Loudness is denoted by Q symbol.

How to calculate Loudness using this online calculator? To use this online calculator for Loudness, enter Sound Intensity (I_s) & Reference Intensity (I_ref) and hit the calculate button. Here is how the Loudness calculation can be explained with given input values -> 48.75061 = 10*log10(75/0.001).

FAQ

What is Loudness?

Loudness refers to how loud or soft a sound seems to a listener. The loudness of sound is determined, in turn, by the intensity of the sound waves. Intensity is a measure of the amount of energy in sound waves and is represented as Q = 10*log10(I_s/I_ref) or Loudness = 10*log10(Sound Intensity/Reference Intensity). Sound Intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area & Reference Intensity is the lowest intensity of sound a person with normal hearing can perceive.

How to calculate Loudness?

Loudness refers to how loud or soft a sound seems to a listener. The loudness of sound is determined, in turn, by the intensity of the sound waves. Intensity is a measure of the amount of energy in sound waves is calculated using Loudness = 10*log10(Sound Intensity/Reference Intensity). To calculate Loudness, you need Sound Intensity (I_s) & Reference Intensity (I_ref). With our tool, you need to enter the respective value for Sound Intensity & Reference Intensity 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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