Sound Propagation Indoor

Overview

Engineering reference data for Sound Propagation Indoor 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

Worked Example

The following calculation demonstrates how to apply the fundamental sound propagation equations for a source in a reverberant room.

Given:

• Source Sound Power Level ($L_N$): 90 dB
• Total Room Absorption ($A$): 12.2 m² Sabine
• Mean Absorption Coefficient ($\alpha_m$): 0.2
• Directivity Coefficient ($D$): 1 (receiver in the middle of the room)
• Distance from Source ($r$): 2 m

Step 1: Calculate the Room Constant ($R$) The room constant defines the acoustic character of the space. $R = \frac{A}{1 - \alpha_m}$ $R = \frac{12.2 \ \text{m}^2}{1 - 0.2} = 15.25 \ \text{m}^2 \ \text{Sabine}$

Step 2: Calculate the Received Sound Pressure Level ($L_p$) The received level is the sum of direct and reverberant sound energy. $L_p = L_N + 10 \log_{10} \left( \frac{D}{4\pi r^2} + \frac{4}{R} \right)$ $L_p = 90 + 10 \log_{10} \left( \frac{1}{4\pi (2)^2} + \frac{4}{15.25} \right)$ $L_p = 90 + 10 \log_{10} \left( 0.01989 + 0.2623 \right)$ $L_p = 90 + 10 \log_{10} (0.2822)$ $L_p = 90 - 5.5 \approx 84.5 \ \text{dB}$

Note: The result (84.5 dB) is consistent with the value (84.8 dB) from the source material, with minor differences due to rounding in intermediate steps.

References

• Original Source