Directivity Coefficient Sound

Overview

Engineering reference data for Directivity Coefficient Sound in acoustics.

Key Formulas

Speed of Sound

$c = \sqrt{\gamma R T}$

Speed of sound in an ideal gas.

Sound Level

$L = 10 \log_{10}(I/I_0)$

Decibel level.

Wavelength

$\lambda = c / f$

Wavelength = speed / frequency.

Variables

Symbol	Description	Unit
$c$	Speed of sound	m/s
$L$	Sound level	dB
$\lambda$	Wavelength	m
$f$	Frequency	Hz

Directivity Coefficient Table

The directivity coefficient D accounts for the source's position relative to room boundaries. Sound radiating into a full sphere has D = 1, while placement near reflecting surfaces increases D as radiation is concentrated into smaller solid angles.

Practical Example

Given:

• Room constant: $R = 1000 \text{ m}^2 \text{ Sabine}$
• Directivity coefficient: $D = 1$ (source in center of room)
• Distance from source: $r = 1 \text{ m}$

Calculate the ratio:

$\frac{r}{\sqrt{D}} = \frac{1}{\sqrt{1}} = 1 \text{ m}$

Estimate attenuation from the diagram or compute directly:

$L_p - L_N = 10 \log\left(\frac{1}{4\pi(1)^2} + \frac{4}{1000}\right) \approx 10 \text{ dB}$

This 10 dB attenuation represents the reduction from the source's sound power level to the received sound pressure level at the listener's position.

Notes on Room Sound Behavior

Near field vs. far field:

• At short distances from the source ($r$ small), the direct sound term $D/(4\pi r^2)$ dominates. Sound level decreases approximately 6 dB per doubling of distance (inverse square law).
• At large distances, the reverberant term $4/R$ dominates, and sound level becomes nearly uniform throughout the room.

Critical distance ($r_c$) is where direct and reverberant sound are equal:

$r_c = \frac{1}{4}\sqrt{\frac{D \cdot R}{\pi}}$

Beyond this distance, the room's reverberant field controls the sound level at the listener.

References

• Original Source