If the sound pressure level of the entire loudspeaker is measured on this straight line (or hyperbola), then the phase difference is recorded correctly.

**It's a bit more problematic when 3 sound sources are being used (pictured
below).**

In the easiest case we are interested in the sound pressure level exactly on the axis a (i.e. right in-between the midrange drivers). Now the problem arises that - depending on the distance to the loudspeaker - the phase difference between tweeter and mid / bass driver changes according to the distance.

The further away the listener is located from the loudspeaker the smaller the phase difference, that depends on the difference of x - a.

The sound path difference is:

x-a = square root (a^{2} + h^{2}) - a

An example concerning our PA speaker D3300-2-66, where h is approx. 29 cm:

Distance | Difference in distance | Phase difference at 2 kHz |

0.7 m | 6 cm | 122 degrees |

1.0 m | 4.1 cm | 87 degrees |

1.7 m | 2.5 cm | 52 degrees |

2 m | 2.1 cm | 44 degrees |

3 m | 1.4 cm | 30 degrees |

5 m | 0.8 cm | 18 degrees |

7 m | 0.6 cm | 13 degrees |

10 m | 0.4 cm | 9 degrees |

The table shows clearly that developing the speaker with a microphone distance of 70 cm is absolute nonsense when later the average listening distance is 5 metres. In later applications the phase difference between tweeter and bass driver would be 122 degrees - 13 degrees = 109 degrees different to the design in the lab.

Here we have different solutions:

a) measuring takes place in a very large room that needs to have a height and width of at least 2 x 3 = 6 metres, since reflections shouldn't be disturbing.

b) one amplifier per channel is being used that contains an adjustable delay unit to ensure that phase shifts in lab measuring are compensated for.

c) the sound path distance is compensated by moving the bass drivers forward.
Measuring then takes place at a distance where the phase difference is the
same as in a later, real life application.

In case the indented sound distance of the PA speaker is 7 metres, the phase
/ sound travel difference will be 0.6 cm; if you then wish to measure at a
distance of 1.7 metres the phase / sound travel difference would be 2.5 cm,
meaning that the bass driver needs to be put forward by 1.9 cm. That's exactly
how we are going to proceed with the speakers to be analysed.

We decided to use solution c) for our design. One of these corrections needs to be used when drivers (at least three) are spread widely over the baffle and are supposed to transmit medium and high frequencies.

After extensive research the crossover designed for the PA speaker D3300-2-606
represented a well balanced compromise.

**Picture left:**

Frequency response

depending on listening

respectively measuring

position.

The sound pressure

level was chosen

arbitrarily.

It's noticeable that the frequency response is different at varying distances.
Originally, the differences were much bigger: when the upper curve was spot
on, the lowest curve (where the phase from tweeter to bass driver is shifted
by 80 degrees) showed cancelling-outs at a specific crossover location.

After extensive design work the dependency is perfectly low: At 1 metre distance a small irregularity becomes apparent at approx. 1.3 kHz, that doesn't become much more prominent at 14 metres distance at 2 kHz (refer to arrows).

If required we'll provide a calculator to help you doing this.