# cone size vs lowest frequency table!?

#### soundnovice

##### Member
anybody have a table for cone size and possible/achievable lowest frequency? assume zero Xmax

#### theAnonymous1

##### Member
Zero xmax = zero output. How can a driver produce any sound if it can't move?

#### David_Web

##### Member
That would be 0dB or infinite frequency for *any* size as there is no sound with zero displacement.

You can calculate the output of a direct radiator here, also includes formulas:
Piston Excursion calculator

#### FoMoCo

##### Member
There isn't one. To make one you'd have to have a desired SPL and reference displacement. Even then, it would need to be based on cone area, not diameter. To make things more complicated, you also need a common box topology.

However, this calculator may be of some use: Piston Excursion calculator

#### marco_gea

##### Member
Depends

Hello,

in order to answer that question, you have to define the peak SPL that you want to achieve, and the cone excursion (Xmax) that you wish to tolerate (arguably, the lower the better for the quality of the reproduction).

The equations that govern this are:

Power(acoustic) = 10^[(SPL-110)/20)]
Sd(m2) = Power * 4*Pi / [(2*Pi*Freq)^2 * rho * Xmax)

For instance, if you impose the following rather strict requirements of:

Peak SPL = 110 dB/W(1m)
Xmax = 2 mm (= 0.002 m)

you get:

20 Hz: Sd = 3300 cm2 (i.e. effective diameter = 65cm ! - here's what Fostex's nominal 80cm woofers are for)
30 Hz: Sd = 1470 cm2 (~ the typical 18" woofer)
40 Hz: Sd = 830 cm2 (~ the typical 15" woofer)

and so on (for 100Hz "bass", a nominal 6.5" unit suffices ;-) )

Of course, if you relax the SPL or Xmax requirements, you may get away with using smaller woofers (but at the cost of decreased realism, both because of lower uncompressed SPL and because the larger the excursion, the higher the IM distortion and the less linear the BL and other T-S parameters).

Hope this helps.

Marco

#### soundnovice

##### Member
Hello,

in order to answer that question, you have to define the peak SPL that you want to achieve, and the cone excursion (Xmax) that you wish to tolerate (arguably, the lower the better for the quality of the reproduction).

The equations that govern this are:

Power(acoustic) = 10^[(SPL-110)/20)]
Sd(m2) = Power * 4*Pi / [(2*Pi*Freq)^2 * rho * Xmax)

For instance, if you impose the following rather strict requirements of:

Peak SPL = 110 dB/W(1m)
Xmax = 2 mm (= 0.002 m)

you get:

20 Hz: Sd = 3300 cm2 (i.e. effective diameter = 65cm ! - here's what Fostex's nominal 80cm woofers are for)
30 Hz: Sd = 1470 cm2 (~ the typical 18" woofer)
40 Hz: Sd = 830 cm2 (~ the typical 15" woofer)

and so on (for 100Hz "bass", a nominal 6.5" unit suffices ;-) )

Of course, if you relax the SPL or Xmax requirements, you may get away with using smaller woofers (but at the cost of decreased realism, both because of lower uncompressed SPL and because the larger the excursion, the higher the IM distortion and the less linear the BL and other T-S parameters).

Hope this helps.

Marco

selecting 110dB SPL and Xmax of 2mm makes good reference values.
with the formula you have mentioned i should be able to calculate for other different types of driver sizes/xmax etc.
thanks a lot #### goldyrathore

##### Member
selecting 110dB SPL and Xmax of 2mm makes good reference values.
Take into account room too. Below the first room mode there is a lot of spl gained. You may be able to relax the reference values. The smaller the room the more the spl gain.

#### soundnovice

##### Member
Take into account room too. Below the first room mode there is a lot of spl gained. You may be able to relax the reference values. The smaller the room the more the spl gain.
intention was to understand the relationship between, conesize, xmax and lowest frequency achievable at a specific SPL. ofcourse room mode will need to be taken into account for further design of actual sub