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|Today, 08:26 PM||#7961|
So i'm all for a CD/horn combo reaching at least down to there.
Big question in my mind is whether a large horn+large format CD is better taken down really low, than using smaller cone mids to bridge to up to a higher CD xover point. (using small mids from say 250Hz up)
So far, on my latest syn builds which have added small mids to raise the CD cross point, i say resoundingly no to the lower CD idea so prevalent today....
But maybe that's just the syn/meh magic working...dunno...
|Today, 08:31 PM||#7962|
Join Date: Mar 2010
THE PURPOSE OF A HORN
It can be useful to look at the purpose of the horn before looking at the theory. Where are horns used, and for what?
Throughout the history of electroacoustics, there have been two important
• Loading of the driver
• Directivity control
You would also think that increasing the output would be one aspect of horns, but this is included in both. Increasing the loading of the driver over that of free air increases efficiency and hence the output, and concentrating the sound into a certain solid angle increases the output further.
Loading of the Driver
The loudspeaker, which is a generator of pressure, has an internal source impedance and drives an external load impedance. The air is the ultimate load, and the impedance of air is low, because of its low density.
The source impedance of any loudspeaker, on the other hand, is high, so there will be a considerable mismatch between the source and the load. The result is that most of the energy put into a direct radiating loudspeaker will notreach the air, but will be converted to heat in the voice coil and mechanical resistances in the unit. The problem is worse at low frequencies, where the size of the source will be small compared to a wavelength and the source will merely push the medium away. At higher frequencies, the radiation from the source will be in the form of plane waves that do not spread out. The load, as seen from the driver, is at its highest, and the system is as efficient as it can be. If you could make the driver radiate plane waves in its entire operating range, efficient operation would be secured at all frequencies. The driver would work into a constant load, and if this load could be made to match the impedances of the driver, resonances would be suppressed.
This is because the driver is a mechanical filter, which needs to be terminated in its characteristic impedance, ideally a pure resistance. If the driver is allowed to radiate plane waves, resistive loading is secured. The easiest way to make the driver radiate plane waves is to connect it to a long, uniform tube. But the end of the tube will still be small compared to a wavelength at low frequencies. To avoid reflections, the cross section of the tube must be large compared to a wavelength, but, at the same time, it must also be small to fit the driver and present the required load. To solve this dilemma, you need to taper the tube.
When you do this, you can take radiation from the driver in the form of plane waves and transform the high pressure, low velocity vibrations at the throat into low pressure, high velocity vibrations that can efficiently be radiated into the air. Depending on how the tube flares, it is possible to present a load to the driver that is constant over a large frequency range.
The directivity of a cone or dome diaphragm is largely uncontrolled, dictated by the dimensions of the diaphragm, and heavily dependent on frequency, becoming sharper and sharper as frequency increases.
You can solve this problem by using multiple driving units and digital signal processing, but a far simpler and cheaper way to achieve predictable directivity control is to use a horn. The walls of the horn will restrict the spreading of the sound waves, so that sound can be focused into the areas where it is needed, and kept out of areas where it is not.
Directivity control is most important in sound reinforcement systems, where a large audience should have the same distribution of low and high frequencies, and where reverberation and reflections can be a problem. In a studio or home environment, this is not as big a problem.
WHAT IS CUTOFF?
Both exponential and hyperbolic horns have a property called cutoff. Below this frequency, the horn transmits nothing, and its throat impedance impedance is purely reactive. But what happens at this frequency? What separates the exponential and hyperbolic horns from the conical horn that does not have a cutoff frequency?
To understand this, you first must look at the difference between plane and spherical waves. A plane wave propagating in a uniform tube will not have
any expansion of the wave-front. The normalized acoustical impedance is uniform and equal to unity through the entire tube.
A propagating spherical wave, on the other hand, has an acoustical impedance that changes with frequency and distance from the source.
At low frequencies and small radii, the acoustical impedance is dominated by reactance. When kr = 1—i.e., when the distance from the source is λ/2π —the reactive
and resistive parts of the impedance are equal, and above this frequency, resistance dominates.
The difference between the two cases is that the air particles in the spherical wave move apart as the wave propagates; the wave-front becomes stretched.
This introduces reactance into the system, because you have two components in the propagating wave: the pressure that propagates outward, and the pressure that stretches the wave-front. The propagating pressure is the same as in the non-expanding plane wave, and gives the resistive component of the impedance.
The stretching pressure steals energy from the propagating wave and stores it, introducing a reactive component where no power is dissipated. You can
say that below kr = 1, there is reactively dominated propagation, and above kr = 1 there is resistive dominated propagation.
If you apply this concept to the conical and exponential horns by looking at how the wave-fronts expand in these two horns, you will see why the cutoff phenomenon occurs in the exponential horn. You must consider the flare rate of the horn, which is defined as (rate of change of wave-front area with distance)/(wave-front area).
In a conical horn, the flare rate changes throughout the horn, and the point where propagation changes from reactive to resistive changes with frequency throughout the horn.
In an exponential horn, the flare rate is constant. Here the transition from reactive to resistive wave propagation happens at the same frequency throughout the entire horn. This is the cutoff frequency. There is no gradual transition, no frequency dependent change in propagation type, and that’s why the change is so abrupt.
Last edited by Ro808; Today at 08:36 PM.
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