The question as to why a large speaker doesn't perform well at high frequencies has been asked many times.  To one with a knowledge of the dynamics of a loudspeaker, the answer is easily understood but not so by one without such acuity.  There are two basic properties of a loudspeaker that are responsible for this.  One is the reactance of the voice coil and the other is the physical mass of the moving system.  The more predominant of the two is the coil reactance which increases dramatically with frequency.

Most speaker box design software takes the reactance part into account when calculating the response curve.  In Bass Box Pro, this can be seen by not including the voice coil inductance in the parameters.  Without the inclusion of that inductance, the curve is a straight line in the higher register above a few hundred hertz to 20 khz.

This inductance acts like a voltage divider between the resistive (real) component and the reactive (inductive reactance/imaginary) component of the coil.  An experiment was done to show this, using a 1 mh coil with a dc resistance of 0.43 ohms wired in series with a resistor of 5.25 ohms.  The sum of the two resistances is 5.68 ohms and in the region of that of a typical 8 ohm woofer. 

Using LMS, Loudspeaker Management System by LinearX, the impedance of the coil and series resistor was plotted.  The LMS uses a relatively constant current method by using a 500 ohm internal series resistor.

While this curve may show what transpires in a coil with a 5 ohm internal resistance, it deviates somewhat from reality.  The current through a speaker varies and there is a back emf due to the motion of the voice coil, not to mention the effect of the mass of the moving system and the acoustical properties thereof. (see the second photo)

 

 

 

 

 

 

The blue trace is the 1.0 mh coil by itself.  The vertical scale on the left is OHMS.  Ideally, this trace would be a straight line but it curves in the low frequency region due to the internal resistance of the wire.  The red curve is that with the coil and resistor series network. The effect of added resistance is clear.

In the table below, the impedance is that of the coil and series resistor.  These two are two sides of a voltage divider.  The resistive component is constant but the reactive component rises.  The table values are based on a constant current through the system and the rolloff is calculated by the voltage drop across resistive and reactive components.

In reality, the current will vary also thus changing this result constantly.  Current variation is the result of impedance changes and is frequency dependant.

FREQ IMPEDANCE ROLLOFF
hz ohms dB
1k 7.59 -2.56     -3
2k 11.86 -6.39     -6
4k 22.47 -11.95     -12
8k 46.21 -18.21     -18

 

 

 

 

 

One fella in an audio forum explained to another why the high frequency rolloff of a large speaker doesn't behave as predicted by stating such things as shown in the photo below.  Another culprit is transverse waves propagating along the cone, much like ripples in a pool after a stone is dropped therein.  Any material will transmit sound through its medium, the effect and quantity of which is governed mainly by the density of the medium.  When one thinks of all the things which can affect the dynamics of a loudspeaker, it's a wonder it works as well as it does.

 

The Second Photo

This is a really cool piccy.  It shows what happens to a speaker cone at high frequencies.  This could explain why the measured frequency response of a speaker, even when done near field, deviates strongly from that predicted by the above experiment.  Typically, a 12 inch speaker will show a strong high frequency output up to about 6 khz. albeit anything but flat.  Many a 10 inch speaker has shown a 10 to 15 dB peak an octave wide centered at about 3 khz. (2khz to 4 khz).  This seems to coincide with the wavelength at 3 khz, 4.5 inches which is the diameter of the frustrum of the cone midway between the apex and the annulus.  On 12 inch units, this peak will shift to about 2.5 khz.

Of course, there are ways to tame this; the above refers to paper cones.  Cone breakup, though, is more difficult to control.  Materials such as woven Kevlar help but the best I've seen are ceramic diaphragms but they're grossly expensive and the largest I've seen is about 5 inches in diameter.  Larger cones made of a poly something or other sandwiched between Kevlar and/or carbon fibre layers are very rigid; the center part being honeycombed.

 

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