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Loudness Formula

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Loudness is a measure of the amplitude or intensity of a sound wave, typically measured in decibels, which determines the perceived volume of the sound. Check FAQs

Q = 10 \cdot \log 10 (\frac{I s}{I ref})

Q - Loudness?I_s - Sound Intensity?I_ref - Reference Intensity?

Loudness Example

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Here is how the Loudness equation looks like with Values.

Here is how the Loudness equation looks like with Units.

Here is how the Loudness equation looks like.

48.7506 = 10 \cdot \log 10 (\frac{75}{0.001})

48.7506dB = 10 \cdot \log 10 (\frac{75W/m²}{0.001W/m²})

48.7506 = 10 \cdot \log 10 (\frac{75}{0.001})

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Loudness Solution

Follow our step by step solution on how to calculate Loudness?

FIRST Step Consider the formula

Q = 10 \cdot \log 10 (\frac{I s}{I ref})

Next Step Substitute values of Variables

∴

Q = 10 \cdot \log 10 (\frac{75W/m²}{0.001W/m²})

Next Step Prepare to Evaluate

∴

Q = 10 \cdot \log 10 (\frac{75}{0.001})

Next Step Evaluate

∴

Q = 48.750612633917dB

LAST Step Rounding Answer

∴

Q = 48.7506dB

Loudness Formula Elements

Variables

Functions

Loudness

Loudness is a measure of the amplitude or intensity of a sound wave, typically measured in decibels, which determines the perceived volume of the sound.

Symbol: Q

Measurement: SoundUnit: dB

Note: Value can be positive or negative.

Formulas to find Loudness

Sound Intensity

Sound Intensity is a measure of the amplitude or loudness of a sound wave, typically measured in decibels, and is a fundamental property of wave propagation.

Symbol: I_s

Measurement: IntensityUnit: W/m²

Note: Value can be positive or negative.

Formulas to find Sound Intensity

Reference Intensity

Reference Intensity is the measure of the amplitude or magnitude of a wave, indicating the amount of energy it carries or its loudness.

Symbol: I_ref

Measurement: IntensityUnit: W/m²

Note: Value can be positive or negative.

Formulas to find Reference Intensity

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)

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How to Evaluate Loudness?

Loudness evaluator uses Loudness = 10*log10(Sound Intensity/Reference Intensity) to evaluate the Loudness, Loudness formula is defined as a measure of the intensity of sound, which is a subjective perception of the pressure and frequency of sound waves, and is typically expressed in decibels, providing a way to quantify and compare the loudness of different sounds. Loudness is denoted by Q symbol.

How to evaluate Loudness using this online evaluator? To use this online evaluator for Loudness, enter Sound Intensity (I_s) & Reference Intensity (I_ref) and hit the calculate button.

FAQs on Loudness

What is the formula to find Loudness?

The formula of Loudness is expressed as Loudness = 10*log10(Sound Intensity/Reference Intensity). Here is an example- 48.75061 = 10*log10(75/0.001).

How to calculate Loudness?

With Sound Intensity (I_s) & Reference Intensity (I_ref) we can find Loudness using the formula - Loudness = 10*log10(Sound Intensity/Reference Intensity). This formula also uses Common Logarithm (log10) function(s).

Can the Loudness be negative?

Yes, the Loudness, measured in Sound can be negative.

Which unit is used to measure Loudness?

Loudness is usually measured using the Decibel[dB] for Sound. Bel[dB], Neper[dB] are the few other units in which Loudness can be measured.

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Loudness Formula

Loudness Example

Loudness Solution

Loudness Formula Elements

Other formulas in Wave Characteristics category

How to Evaluate Loudness?

FAQs on Loudness

Variable Name