Loudness Distance Calculator

Formula

The formula to calculate the Loudness at a New Distance (L₂) is:

\[ L_{2} = \frac{L_{1}}{\left(\frac{d_{2}}{d_{1}}\right)^{2}} \]

Where:

Loudness at New Distance (L₂): The perceived loudness of a sound at a new distance from the source.
Original Loudness (L₁): The initial loudness of the sound at the original distance.
Original Distance (d₁): The initial distance from the sound source.
New Distance (d₂): The new distance from the sound source.
Significance: Helps in understanding how sound propagates over distance, which is important in acoustics, audio engineering, and environmental noise control.

Let's say the original loudness (L₁) is 80 dB, the original distance (d₁) is 2 meters, and the new distance (d₂) is 4 meters. Using the formula:

\[ L_{2} = \frac{80}{\left(\frac{4}{2}\right)^{2}} = \frac{80}{4} = 20 \]

So, the Loudness at the New Distance (L₂) is 20 dB.