How to measure loudspeaker power response?

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Who knows?

I can think that this requires the integration of a set of local sound pressure measurements. But I do not know how.

The software I use (Boxsim), estimates the acoustic power output. If the frequency response measurements match the predictions, at different angles, I infer that the software prediction about the acoustic power is correct.
I can not do more.

But in your case probably the acoustics of the room dominates the speakers characteristics. REW is a useful software for room acoustics.
 
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Bring the speaker and mic toward the middle of the room across the diagonal, and at half height. This way you can increase the reflected distance. Try to measure from far enough to allow the diffraction from the speaker to combine in the expected way. You will be able to measure highs and down to some lower frequency.
 
Floyd toole/harman take 72 measurements in an anechoic chamber: 36 on one axis and 36 on a perpendicular axis. See page 7 for the setup:

https://www.harman.com/sites/default/files/LoudspeakersandRoomsPt2_0.pdf

This data is processed in various ways, but for the power response estimate I believe measurements must be weighted when averaged. There is a higher density of measurements on-axis compared to 90 deg off axis and you must compensate for this.

I do something similar to Harman but I have simplified the process somewhat:

-Put the speaker on a 25ft pole with the mic 1m away (I don't have an anechoic chamber)

-take measurements 360deg on one axis and average the unweighted data

-take measurements 360deg on the perpendicular axis and average the unweighted data separately

Then I compare the curves. If they are in agreement I consider each curve to be a good estimate of power response.

I haven't yet built a speaker where the curves disagree. I imagine this might be an issue with towers, or side firing woofers, etc
 
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In-room quasi-anechoic measurements are reasonably easy to perform, at least up to 90deg laterally and vertically. Most modern speakers are omni anyway below 400Hz so why bother with more prescision?

Princeton university doesn't publish directivity below 500Hz, obviously because they have a too small chamber. 3D3A Lab at Princeton University

Klippel offers a nearfield 3d scanner system, which can calculate 3D dispersion down to bass. Price is around 65.000€ Near Field Scanner System (NFS)
 
In-room quasi-anechoic measurements are reasonably easy to perform, at least up to 90deg laterally and vertically. Most modern speakers are omni anyway below 400Hz so why bother with more prescision?

Princeton university doesn't publish directivity below 500Hz, obviously because they have a too small chamber. 3D3A Lab at Princeton University

Klippel offers a nearfield 3d scanner system, which can calculate 3D dispersion down to bass. Price is around 65.000€ Near Field Scanner System (NFS)

On many speakers the directivity changes substantially below 400hz. If you were making a 3-way speaker, for example, it might be helpful to have power data at lower frequencies.

Interesting system by klippel. I would be curious to see how it compares to free field, and whether it's really a perfect substitute.

Measuring on a pole/tower works great and costs very little. Even without gating there is only a small amount of ripple, and the environmental noise can be filtered out by averaging many measurements.
 
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