This decibel distance calculator is used to calculate how the sound pressure level (SPL) changes as you move closer or farther away from the source.
The calculator typically requires you to input the initial sound level (in decibels), the initial distance, and either the final distance or the final sound level. It then uses the inverse square law to calculate the missing value, which is the final sound level or distance.
When you know that a sound source has an initial level of 100 dB at a distance of 1 meter, and you want to find the sound level at 2 meters, you can input these values into the calculator. It will then use the formula to determine that the sound level at 2 meters is approximately 94 dB.
Decibel Distance Calculator
| Initial Distance (m) | Initial Sound Level (dB) | Final Distance (m) | Final Sound Level (dB) |
|---|---|---|---|
| 1 | 100 | 2 | 94.0 |
| 1 | 100 | 5 | 86.0 |
| 1 | 100 | 10 | 80.0 |
| 1 | 100 | 20 | 74.0 |
| 2 | 94 | 4 | 88.0 |
| 2 | 94 | 6 | 84.0 |
| 2 | 94 | 10 | 80.0 |
| 2 | 94 | 15 | 76.0 |
| 5 | 85 | 10 | 79.0 |
| 5 | 85 | 15 | 76.0 |
| 5 | 85 | 20 | 73.0 |
| 5 | 85 | 30 | 70.0 |
| 10 | 80 | 20 | 74.0 |
| 10 | 80 | 30 | 71.0 |
| 10 | 80 | 50 | 67.0 |
| 10 | 80 | 100 | 64.0 |
| 15 | 78 | 30 | 72.0 |
| 15 | 78 | 50 | 69.0 |
| 15 | 78 | 75 | 66.0 |
| 15 | 78 | 100 | 63.0 |
| 20 | 75 | 40 | 69.0 |
| 20 | 75 | 60 | 66.0 |
| 20 | 75 | 80 | 63.0 |
| 20 | 75 | 100 | 60.0 |
Decibel Distance Calculation Formula
L2 = L1 - 20 log10(d2/d1)Where:
- L1 is the initial sound level (in decibels)
- d1 is the initial distance from the source
- L2 is the final sound level (in decibels)
- d2 is the final distance from the source
Given a sound source producing 100 dB at 1 meter, calculate the sound level at 10 meters:
L2 = 100 – 20 log10(10 / 1)
L2 = 100 – 20 1
L2 = 80 dB
This formula demonstrates that for every doubling of distance, the sound level decreases by approximately 6 dB in free-field conditions.
To use this formula, you need to know three out of the four variables. If you know the initial sound level (L1), the initial distance (d1), and the final distance (d2), you can calculate the final sound level (L2) using the formula.
How to Calculate Decibels at Distance?
- Determine the initial sound level (in decibels) and the initial distance from the source.
- Decide on the final distance at which you want to calculate the sound level.
- Plug the values into the decibel distance formula: L2 = L1 – 20 log10(d2/d1)
- Solve the equation to find the final sound level (L2).
When the initial sound level is 100 dB at a distance of 1 meter, and you want to find the sound level at 5 meters, you would plug in the values as follows:
L2 = 100 – 20 log10(5/1)
L2 = 100 – 20 × 0.699
L2 = 100 – 13.98
L2 = 86.02 dB
At a distance of 5 meters, the sound level would be approximately 86 dB.
A loudspeaker produces 110 dB at 1 meter. Calculate the sound level at 50 meters:
L1 = 110 dB, r1 = 1 meter
r2 = 50 meters
L2 = 110 – 20 log10(50 / 1)
= 110 – 20 1.69897
= 110 – 33.9794
= 76.0206 dB
How Far Do 100 Decibels Travel?
When initial sound level is 100 dB at 1 meter, it will drop to 60 dB at a distance of approximately 100 meters.
The distance that 100 decibels can travel depends on several factors, such as the environment, obstacles, and atmospheric conditions. However, we can use the decibel distance formula to estimate the distance at which the sound level drops to a certain level.
Let’s say we have a sound source that produces 100 dB at a distance of 1 meter. We want to find the distance at which the sound level drops to 60 dB. We can rearrange the formula to solve for d2:
L2 = L1 – 20 log10(d2/d1)
60 = 100 – 20 log10(d2/1)
20 log10(d2/1) = 40
log10(d2/1) = 2
d2/1 = 10^2 = 100
d2 = 100 meters
What is the 6 dB Rule for Distance?
The 6 dB rule for distance is a simplified way to estimate the change in sound level when the distance from the source is doubled or halved. It states that:
- When the distance from the sound source is doubled, the sound level decreases by approximately 6 dB.
- When the distance from the sound source is halved, the sound level increases by approximately 6 dB.
This rule is based on the inverse square law and the logarithmic nature of decibels. Since decibels increase exponentially, a 6 dB change corresponds to a fourfold change in sound intensity.
For example, if a sound source has a level of 100 dB at a distance of 1 meter, and you move to a distance of 2 meters, the sound level will drop by approximately 6 dB, resulting in a level of 94 dB. Conversely, if you move from 2 meters to 1 meter, the sound level will increase by 6 dB, reaching 106 dB.
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