Propagation of Sound Outdoors

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The sound 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:

L_p = L_w + 10 log[(Q/4π)(1/r₁²+ 1/r₂²+ ...+1/r_n²) + 4/R]     (1)

or modified for a single source:

L_p = L_w + 10 log(Q/(4π r²) + 4/R)  (1b)

where

L_p = sound pressure level (dB)

L_w  = sound 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: 

L_p = L_w + 10 log(1/(4π r²) 

   = L_w - 10 log( 4 π r²)       (2)

since

Q  = 1

R ≈ ∞

(2) can also be expressed as: 

L_p = L_w - 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 affecting 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: 

L_p = L_w - 20 log r + K' + DI - A_a - A_b      (3)

where

DI = directivity index

A_a = attenuation due to atmospheric conditions

A_b = 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 (intergral) to express the sound pressure as:

L_p = L_w - 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.

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Related Topics

• Acoustics - Room acoustics, acoustic properties - decibel A, B and C - Noise Rating (NR) curves, sound transmission, sound pressure, sound intensity, attenuation and more ..
• Noise and Attenuation - Noise is usually defined as unwanted sound - noise, noise generation, silencers and attenuation in HVAC systems

Related Documents

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• L_dn - Day and Night Sound Level - The EPA has defined an A-weighted sound level day and night equivalent for a 24 hour period
• Outdoor Ambient Sound Levels - Outdoor ambient sound level (dBA) in rural and urban business and industrial environments with or without limited traffic
• Propagation of Sound Outdoors and Partial Barriers - The transmission of sound through and around outdoor barriers - Fresnel Number
• Voice Level and Distance - The voice level at various distances