# Low Frequency output - technical questions re Sd and Xmax

Discussion in 'Amps and Cabs [BG]' started by alexclaber, Jul 28, 2005.

1. ### alexclaberCommercial User

Jun 19, 2001
Brighton, UK
Director - Barefaced Ltd
Pondering speaker design...

I had come to the conclusion that the low frequency output of a speaker was down to the area (Sd) multiplied by the excursion (Xmax). Makes sense, huh?

But it's just dawned on me that there's more to it that how much air the cone is moving, it's about how the air it moves directly, couples with the air in the rest of the room (like a bass horn has to have huge area to get perfect coupling).

So although Sd x Xmax gives the maximum generic LF output, are the lowest lows also dependant on the total Sd of the rig, because as the total cone area increases, so the size of the source vs the size of the wave (at low frequencies) becomes more appropriate? Or does the area vs wavelength thing only affect dispersion characteristics (which does affect efficiency but in a roundabout way)?

Alex

2. ### bgavin

May 3, 2001
Orangevale, CA 95662
Loudness = volume of air moved. Sd * Xmax = displacement

Efficiency = Amount of displacement per power unit, i.e. 1 watt at 1 meter.

Total loudness = displacement at maximum input power.

Cone movement = 4x increase per octave down.

*****

For work to be done, power is developed across a resistance. The strongest man in the world is not doing any work if he is doing curls with no bar and no weights. He is just flapping his arms around and developing no power. Ditto for a direct radiator.

A speaker is a high impedance device. It has to operate into a high resistance for full power transfer. Flapping in the air is akin to paddling a canoe with a tea spoon. You can't get any "bite" into the water to do work (move the canoe). A 426 hemi sitting up on blocks can spin at 7,000 RPM but it isn't doing any work with the tires off the ground.

A bass horn is an impedance matching device (acoustic transformer). It transforms the low atmospheric load into a high resistance in the horn throat. The driver has something solid to bite into, and effectively transfers power.

The bass horn has a very large effective Sd which moves a lot of air, but does so without the performance penalty of using a very large cone.

Directional characteristics of a direct radiator are determined by the piston circumference in relation to the wave length. When the wave length is equal or less than the circumference, the driver is highly directional (beaming). It would be interesting to see a 41 Hz bass horn with a circumference of 27 feet, and see if it beams.

3. ### steveksux

Mar 23, 2005
Detroit area, Troy, MI
Depends a lot on cab tuning too, at some freqs there's more output from the port than the front of the speaker, others the cone's barely moving cause its motion is supressed by the backwave, and somewhere below resonant freq, the back wave reinforces the cone movement and HELPS it move, begging for it to be overexcursed.

Something like that.

But more driver area gives you lower freq resp in general, helps reproduce the larger waveforms. You can get more driver area by going with a bigger speaker, or multiple smaller speakers.

Randy

4. ### ESP-LTD

Sep 9, 2001
Idaho
But of course, those simple explanations don't include the effects of ohmitude and wattishnicity, which are the more common concerns in cabinet design.