Sound Attenuation Ducts

Overview

Engineering reference data for Sound Attenuation Ducts 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

Duct Splitting Sound Attenuation

When a duct splits into multiple terminals, the sound power level is reduced proportionally to the volume of air distributed to each terminal. For equal terminal splits, the attenuation follows a logarithmic relationship.

Splitting into Equal Terminals

For a duct splitting into $n$ equal terminals, the sound power attenuation to each terminal is:

$\Delta L_N = 10 \cdot \log_{10}(n)$

Where:

• $\Delta L_N$ = sound attenuation (dB)
• $n$ = number of equal terminals

Common Split Attenuation Values

Example Calculation

Problem: A duct splits into four equal terminals. What is the sound attenuation to each terminal?

Solution:

$\Delta L_N = 10 \cdot \log_{10}(4) = 10 \cdot 0.602 = 6 \text{ dB}$

Each terminal receives approximately 6 dB less sound power level than the original duct.

Key Properties

• Attenuation applies to sound power level, not sound pressure level
• For unequal splits, attenuation is proportional to the volume ratio: $\Delta L_N = 10 \cdot \log_{10}\left(\frac{Q_{total}}{Q_{terminal}}\right)$ where $Q$ is the volume flow rate
• The total sound power is conserved across all terminals
• Higher frequencies may experience additional attenuation due to directional effects at junctions

References

• Original Source