Line Propagation Spreading Loss

**Strutt|Propagation|Line Source** provides the correction for cylindrical sound radiation from a line source, given the perpendicular distance from the source (d) in metres.

Distance correction can be calculated for either finite or infinite line sources and coherent sources (e.g. tonal noise source) or incoherent sources (broadband noise source e.g. traffic, pipe, conveyor belt).

**Infinite Line Source** calculates the sound pressure level (SPL) for the following:

__Incoherent Line Source__ is calculated using

`L_p = L prime _W - 6 - 10log_10 d`

__Coherent Line Source__ is calculated using

`L_p = L prime _W - 8 - 10log_10 d`

**Finite Line Source** calculates the SPL for the following:

__Incoherent Line Source__ is calculated using

`L_p = L prime _W - 8 - 10log_10 d + 10log_10 [2tan^(-1)(L/(2d))]`

Where `L` is source length and `d` is perpindicular distance to receiver.

A __Coherent Line Source__ of finite length has the same SPL as a finite length incoherent source, for large distances from the source compared with the source length (`d > L//2`).

Close to a coherent source of finite length (`d < L//10`), the SPL normal to the centre of the source will be the same as for an infinite coherent source.

For distances in between, the SPL for coherent finite length sources is interpolated.

N.B. the sound pressure level `L_p` is calculated using the sound power per unit length `L prime _W ` (`dB//m`), __not__ the overall sound power `L_W` (`dB`).

It should be noted that the Finite Line Source calculation effectively includes an angle of view correction (the `10log_10[2tan^(-1)(L//2d)]` term), while Infinite Line Source does not. If infinite line source is used, a separate Angle of View Correction should be applied if necessary.

The Finite Line Source calculation also assumes that the midpoint of the source is aligned with the receiver location - i.e. that the source is symmetrical around the receiver. If this is not the case, use the infinite line source calculation and the Angle of View correction.

To calculate sound pressure level where the spacing between sources is finite, use the Array of Point Sources calculation.

References:

- Transportation Noise Reference Book p2/8
- Bies, D., Hansen, C., Engineering Noise Control, 3rd Edition, pp188-192

Comments or suggestions to strutt@arup.com