Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Propagation of Sound Outdoors - Attenuation vs. Distance

The propagation of outdoors sound vs. distance and attenuation.

The energy in the propagation direction of the sound is inversely proportional to the increasing surface area the sound propagates through and can be expressed as

Lp = LN + 10 log [(Q / 4 π) (1 / r12+ 1 / r22+ ...+1 / rn2) + 4 / R]                             (1)

or modified for a single source:

Lp = LN + 10 log (Q / (4 π r2) + 4 / R)                                (1b)

where

Lpsound pressure level (dB)

Lsound power level source in decibel (dB)

Q = directivity coefficient (1 uniform spherical, 2 uniform half spherical (single reflecting surface), 4 uniform radiation over 1/4 sphere (two reflecting surfaces, corner)

r = distance from source  (m)

R = room constant (m2)

Single Sound Source - Spherical Propagation

With uniform spherical radiation (1) can be modified to express the sound pressure level from a single sound source as

Lp = LN + 10 log (1 / (4 π r2

   = LN - 10 log (4 π r2)                                   (2)

since

Q  = 1

R ≈ ∞

(2) can also be expressed as: 

Lp = LN - 20 log (r) + K'                            (2b)

where 

K' = -11 (single sound source and spherical radiation) 

Single Sound Source - Hemi-Spherical Propagation

When the sound source propagates hemi-spherically with the source near ground, the constant can be set to 

  • K' = - 8

Note! When the distance - r - from a power source doubles, the sound pressure level decreases with 6 dB. This relationship is also known as the inverse square law.

Other factors that affects the radiation of the sound are the direction of the source, barriers between the source and the receiver and atmospheric conditions. Equation (1) can be modified to: 

Lp = LN - 20 log r + K' + DI - Aa - Ab                                 (3)

where

DI = directivity index

Aa = attenuation due to atmospheric conditions

Ab = attenuation due to barriers

Linear Sound Source

With a linear sound source, like a road or high-way with heavy traffic, (1) can be summarized (integrated) to express the sound pressure as

Lp = LN - 10 log (4 π r)                                   (4)

Note! When the distance - r - from a linear power source doubles, the sound pressure level decreases with 3 dB.

Related Topics

  • Acoustics

    Room acoustics and acoustic properties. decibel A, B and C calculations. Noise Rating (NR) curves. Sound transmission through walls. Calculate sound pressure, sound intensity and sound attenuation.
  • Noise and Attenuation

    Noise is usually defined as unwanted sound - noise, noise generation, silencers and attenuation in HVAC systems.

Related Documents

Search

Search is the most efficient way to navigate the Engineering ToolBox.

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about

We use a third-party to provide monetization technologies for our site. You can review their privacy and cookie policy here.

You can change your privacy settings by clicking the following button: .

Citation

This page can be cited as

  • The Engineering ToolBox (2003). Propagation of Sound Outdoors - Attenuation vs. Distance. [online] Available at: https://www.engineeringtoolbox.com/outdoor-propagation-sound-d_64.html [Accessed Day Month Year].

Modify the access date according your visit.

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter

















































4.10.13

.