- Jul 18, 2019
- North Alabama
6.5" equates to a wavelength of 2065Hz. Being that most are in the 5.25" cone diameter, that is a lot closer to 2571Hz. 8" woofers beam between 1500 to 1800 Hz in general.
You're using full wavelength. Beaming occurs before this. Pretty easy to see; just grab any spec sheet from Scan Speak, and look at where the beaming occurs. Ideally one should use 1/4-wave. But that's not feasible with standard designs. 1/2-wave is "close enough". Full wave is too high.
Here is an example:
Effective Diameter = 138mm (5.4337 inches)
Using this equation:
Speed of sound / effective diameter (half-surround to half-surround) / 2 = ~ beaming
13500 in/s / 5.4337 inches / 2 = 1242Hz
Now, look at the below graphic and you'll see this frequency matches where the divergence is seen in the on/off-axis response:
If you use full wavelength as you suggest, then the beaming point would be at ~2480Hz. Which you can see clearly doesn't match the above and at that frequency the 60-degree off-axis response is already down about 13dB from the on-axis response. That's a big difference in directivity error if you were to place your crossover point that high.
For 8-inch woofers, you can guesstimate:
13500/8/2 = 843Hz. Throw some padding on there for effective diameter.
An example is:
Effective Diameter ~ 6.77 inches (172mm)
13500/6.77/2 = 997Hz
Again, if you used the full wavelength calculation then you'd put your crossover at 2kHz where this speaker has become directional already.
You can use whatever formula you want but as I said: 1/4-wave is the most accurate. 1/2-wave is close enough for standard speakers. Full wave puts you well into the beaming point (especially when you are talking higher angles).
There's a thread somewhere in here where Tom Danley talks about using the 1/4-wave rule for his speakers.