Early Sound Level (Speech)

**Strutt|Auditorium Acoustics|Early Sound Level (Speech)** calculates the early sound level (`G_(0-50ms)`) in a drama auditorium using Barron's modified revised theory.

The modified version of revised theory allows for the case of a proscenium theatre in which a proportion of both the early and late sound energy will escape into the flytower.
The source directivity (`Q`) becomes significant when considering natural speech in a theatre.

In addition, the 'early reflection ratio' (`N`) is used to describe the 'reflection gain' provided by the surfaces of the theatre.
The early reflection ratio is the effective strength of all early energy (up to 50 ms), *including the direct sound* relative to the direct sound.

Hence `N=1` indicates that only the direct sound is present. `N=2` indicates that the early reflections are equal to the direct sound. `N=3` indicates that the cumulative early reflections have twice the strength of the direct sound.

In short, a theatre with a reflection ratio of `N` will have `N-1` strong early reflections.

Refer Section 7.4 and 7.6 Barron for a more-detailed discussion of the early reflection ratio.

The directivity index `DI` is entered in values of decibels (following Strutt's sign conventions), but is converted to geometric directivity factor `Q=10^((DI)/10)` for calculation.

Barron provides some indicative values for vocal directivity as a function of angle, as follows:Angle of listener to speaker: |
0° |
45° |
90° |
135° |
180° |

Directivity index (DI) |
+3.0 |
+2.3 |
-0.6 |
-3.6 |
-1.6 |

Directivity factor (Q) |
2.0 |
1.67 |
0.87 |
0.44 |
0.70 |

Note that the resulting level is expressed as strength (`G`) and can be converted to 'relative loudness' (i.e. relative to the source `L_W`) by subtracting 31 dB.

The early sound is calculated using the following relationship:

`e_r = (100 Q N )/r^2`, where

`r` is the distance from the source.

`Q` is the geometric directivity factor.

`N` is the early reflection ratio.

Strutt calculates the total early sound level as:

`G_(0-50ms)=10log(e_r)`

Reference: Barron *Auditorium Acoustics and Architectural Design*, 2^{nd} edition, Appendix D.3

Comments or suggestions to strutt@arup.com