Sound - Attenuation and the Directivity Coefficient
Calculator for sound pressure level attenuation in a room based on the directivity coefficient, distance from source, and room acoustic properties.
Sound Attenuation Calculator
For a continuing sound source, the sound level in a room is the sum of direct and reverberant sound.
Formula:
Lp = LN + 10 log(D / (4π r²) + 4 / R)
Where:
- Lp = received sound pressure level (dB)
- LN = sound power level from source (dB)
- D = directivity coefficient
- R = room constant (m² Sabine)
- r = distance from source (m)
- π = 3.14159...
Directivity Coefficient (D) Guide
The directivity coefficient depends on the location of the receiver relative to the sound source:
- D = 1: Receiver in center of room (omnidirectional)
- D > 1: Receiver closer to reflecting surfaces (boundary effect increases directivity)
- D < 1: Receiver in free field conditions
Room Constant (R)
The room constant relates to the total room sound absorption (A in m² Sabine) and the room surface area (S in m²):
R = A / (1 - α)
Where α is the average absorption coefficient of the room surfaces.