# Distance Attenuation Calculator

Created by Gabriela Diaz
Last updated: Aug 06, 2022

You can use this distance attenuation calculator to calculate the attenuation in dB of a sound that propagates from its source.

In the text below, we included some of the basics to better understand what distance attenuation is. This is what you'll find:

• Why sound attenuates with distance;
• The sound attenuation formula; and
• A quick way to calculate attenuation in dB.

Enjoy! 🔊

## Sound attenuation with distance

We are familiar with the fact that the further away we are from a sound source, the quieter we perceive it. But why does this happen?

Sound is a form of energy that travels through a medium (e.g., air) and propagates uniformly in all directions, in a spherical or hemispherical fashion. You can imagine something similar to ripples in a lake but three-dimensional.

As the surface area of the sphere grows, the initial amount of energy emitted by the sound source is distributed along this growing surface. Meaning that the further the wavefront is from the source, the greater the radius of the sphere and the lower the amount of energy per unit of area. As a result, the sound level at any point reduces as the distance from the source increases. This is how distance attenuates sound.

Sound is perceived in our ears as changes in air pressure. A practical unit used to quantify this pressure is the sound pressure level (SPL), which is expressed in the decibel logarithm scale. Lower decibel numbers denote softer sounds, whereas higher values indicate louder sounds.

🙋 Do you need to refresh what pressure is and how to calculate it? then we highly suggest checking the pressure calculator.

## Sound attenuation formula

The inverse distance law is used to determine sound pressure level changes at a given distance from the source. This one is also known as the sound attenuation formula, which is provided by:

$\small \text{SPL}_2 = \text{SPL}_1 - 20 \log\left( \cfrac{R_2}{R_1}\right)$

where:

• $\text{SPL}_1$ — Sound pressure level at point 1;
• $\text{SPL}_2$ — Sound pressure level at point 2;
• $R_1$ — Distance from the sound source to point 1; and
• $R_2$ — Distance from the sound source to point 2.

If you only need an approximate estimate of the changes on SPL instead of an accurate number, you can use the inverse square law. This law states that with every doubling of distance from the source, the intensity of a sound decreases four times. In terms of sound pressure level, with every doubling of the distance, the sound pressure level drops around 6 dB.

For instance, if initially at a distance of 2 m from the sound source, the SPL is 70 dB, doubling the distance to 4 m will result in an estimated SPL of 64 dB, about 6 dB less.

🙋 If you enjoyed learning how sound is affected by distance, we recommend checking the sound wavelength calculator, where you'll learn more about the wave nature of sound!

## How to use the distance attenuation calculator

With the distance attenuation calculator, determining how much sound attenuates between two points becomes an easy task. Let us see how to do this:

1. Begin by entering the information associated with Point 1. Indicate the Distance from the source and Sound pressure level in dB.

2. Proceed to enter the Distance from the source for Point 2.

3. The calculator will display Sound pressure level for Point 2 as well as the Difference in SPL.

You could also use this distance attenuation calculator to find how far point 2 needs to be from point 1 for the sound pressure level at point 2 to be of a given value. To do so, repeat step 1 from above and input the desired Sound pressure level at point 2.

Gabriela Diaz
Point 1
Distance from the source
m
Sound pressure level
dB
Point 2
Distance from the source
m
Sound pressure level
dB
Sound level difference
Difference in SPL
dB
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