How do I calculate the off-axis dB SPL of a loudspeaker?

[ianpwilliams]

I am working on an assignment where I create a sound reinforcement system for a particular hypothetical event. I've been hanging speakers from the ceiling, aimed downwards, to try and cover a large area of the audience. I have my dispersions, critical distance etc worked out, but I can't find out how to calculate the difference in dB SPL when moving from on-axis to off-axis.

I found a link on Google Books which talks about using (as an example) this formula:

20log (D / 0.6D) = 4.4dB

but then it talks about taking that result and referring to the particular polar plot of the speaker in question to calculate the actual dB SPL loss or gain. The problem is, the speaker spec sheet I have (for the JBL SRX 715F) does not have a polar plot.

Does anyone have any idea how I can work this out? I would have thought that maybe there might have been some kind of formula for doing it, using the on-axis dB SPL, Q, dispersion etc., but maybe not.

 

[highfigh]

I am working on an assignment where I create a sound reinforcement system for a particular hypothetical event. I've been hanging speakers from the ceiling, aimed downwards, to try and cover a large area of the audience. I have my dispersions, critical distance etc worked out, but I can't find out how to calculate the difference in dB SPL when moving from on-axis to off-axis.

I found a link on Google Books which talks about using (as an example) this formula:

20log (D / 0.6D) = 4.4dB

but then it talks about taking that result and referring to the particular polar plot of the speaker in question to calculate the actual dB SPL loss or gain. The problem is, the speaker spec sheet I have (for the JBL SRX 715F) does not have a polar plot.

Does anyone have any idea how I can work this out? I would have thought that maybe there might have been some kind of formula for doing it, using the on-axis dB SPL, Q, dispersion etc., but maybe not.

AFAIK, there's no way to calculate this just by knowing the on-axis frequency response because the horn has a specific dispersion pattern. JBL has the data because anyone else who would use these, or something like them, would need the data in order to determine whether they will work for their application. I would contact them for this. Also, the distance from the speaker to the mic must be considered.

 

[ianpwilliams]

These are the specs of the SRX715/SRX715F speaker, from the JBL spec sheet.

Specifications:
Frequency Range (-10 dB): 43 Hz – 20 kHz
Frequency Response (±3 dB): 53 Hz – 20 kHz
Coverage Pattern: 75° x 50° nominal
Crossover Modes: Bi-amp / passive, externally switchable
Crossover Frequency: 1.2 kHz
Power Rating
(Continuous1 / Program / Peak): Passive: 800 W / 1600 W / 3200 W
Bi-amp LF: 800 W / 1600 W / 3200 W
Bi-amp HF: 75 W / 150 W / 300 W
Maximum SPL2: 131 dB SPL peak
System Sensitivity (1w @ 1m): 96 dB SPL (passive mode)
LF Driver: 1 x JBL 2265H 380 mm (15 in) Differential Drive
woofer with neodymium-magnet and dual voice-coils
HF Driver: 1 x JBL 2431H 75 mm (3 in) voice-coil, neodymiummagnet
compression driver
Nominal Impedance: Passive: 8 ohms
Bi-amp LF: 8 ohms
Bi-amp HF: 8 ohms
Active Tunings: dbx DriveRack, all models. Settings available at
Enclosure: Trapezoidal, 15 mm, 11-ply birch plywood
Suspension / Mounting: Dual-angle (0° or -10°) 35 mm pole socket
5 x suspension points, M10 or optional fly track kit
(SRX715F only)
Transport: 2 x steel handles
Finish: Black DuraFlex finish
Grille: Powder coated, black, 16-gauge perforated steel with
acoustical transparent charcoal foam backing.
Removable JBL badge and punched JBL logo.
Input Connectors: Neutrik® Speakon® NL-4 (x2)
Dimensions (H x W x D): 711 mm x 439 mm x 406 mm
(28 in x 17.3 in x 16 in)
Net Weight: 22 kg (48 lb)
Optional Accessories: SRX715-CVR: Pull-over padded cover
SRX-FF3: 3x detachable flying fittings
229-00009-01: 3 x 10 mm forged eyebolts

I can't see anything in there which would help me calculate the off-axis dB SPL drop. There are also charts, including frequency response, beamwidth, and directivity index, but these all refer to the dB level of the different frequencies, and I want dB SPL.

 

[lsiberian]

You could do a 2meter measurement at the angle you want in your backyard. This usually works.

 

[ianpwilliams]

How do you mean?

Something which gives me a rough idea of the dB SPL difference would do, I don't need to be really precise.

Would it be worth working out the direct on-axis dB SPL in different directions (and therefore different distances)? Would that give me a rough idea, or would that not be worth doing?

 

[highfigh]

Something which gives me a rough idea of the dB SPL difference would do, I don't need to be really precise.

Well, that's the thing- in order to design a system for a venue, you absolutely must know it's dispersion patterns- vertical and horizontal. Guessing will be successful for only two reasons- your analysis was correct, or you got lucky. A design based on the assumption of narrower dispersion will result in too much overlap and when this happens, you wouldn;t be able to EQ the problems out of the affected area(s). If you assume wider coverage, you'll end up with areas that won't have acceptable SPL and sound quality. JBL has tested these speakers, I assure you. No sound company would ever select a speaker without knowing the patterns.

 

[ianpwilliams]

Oh I know JBL are very thorough in what they do - I've seen that from the endless PDF guides they have, many of which have been extremely useful. I just don't know why the polar plots aren't included in the spec sheets. Incidentally I do know the horizontal and vertical dispersions of all the speakers I am working with, and also the directivity Q factor. Anyway I'll keep looking.

 

[highfigh]

Oh I know JBL are very thorough in what they do - I've seen that from the endless PDF guides they have, many of which have been extremely useful. I just don't know why the polar plots aren't included in the spec sheets. Incidentally I do know the horizontal and vertical dispersions of all the speakers I am working with, and also the directivity Q factor. Anyway I'll keep looking.

I saw the dispersion angles- I guess you could use that as your pattern as a tool if you state that as part of the known data, used for the system design. Whether it's accurate or not, if it's looked at as factual, the outcome on paper should reflect that. If the system response will be measured, I wouldn't make the assumption that it's accurate.