Why most tweeters are crap

Normally manufacturers' provide specifications as data, not graph. i.e.

1. frequency range - 4kHz to 20kHz

2. frequency response - 2kHz to 18kHz +/- 3dB

The above two examples are the correct once while not lying. 

1. When the word "range" is used, +/- x dB is not required 

2. When the word "response" is used, they must provide +/- x dB

A better specification is - total variance between the highest level and the lowest level in the specified range. So that the user will know. This is never before seen. It shows that the audio industry standards is extremely low, which is extremely disappointing.

Else an un-qualified personnel was in charge of specification publications. This means the company is crap or irresponsible.

Regardless, please take a good look at the few tweeters shown in Tweeter Selection, notice how their "response" fluctuate radically yielding in +/- 10dB with a total variance as much as 20dB.

Although only 5 different tweeters are put up, mark these words, not "one" has been found good or up to standard. They are all crap, no matter how expensive or how branded. This is also why all manufacturers' do not dare to publish their anechoic condition's frequency response. 

Most are measured using low detail method. The lack of details of the peaks and troths "mis-lead" the reader. Or else the detailed measurement ha been "smoothed" to reduce the peaks and troths so that it looks good. Again this "mis-lead" the readers. Please see example shown in 1-6 octave versus 1-3 octave

A fundamental scientific explanation to why most tweeters' are crap is: -

A 12" woofer has an effective 28cm in diameter. The highest of the low frequency that it needs to produce is around 100Hz has a wavelength of 3.43 meters long.

( lamda = wavelength = speed of sound divide by frequency = 343.3m / 100Hz = 3.43 meters long) 

then 3.43m wavelength/ 28cm woofer diameter = 12.25 times success digit.

A 5.25" mid-range has an effective 13cm in diameter. The highest frequency that I recommend it should not exceed to produce is around 1kHz (-300Hz range). This is because we do not want it to play into the cone break-up range, because the frequency response is highly radical and not categorized as high-quality. Please see 3D movement of 13.8Hz.

So this time 343.4 / 1000 = 34.34 cm

and that 34.34cm / 13cm = is no more than 2.6 times success digit

Notice it has reduced from 12 times to less than 3 times :(

Finally, 1 inch dome tweeters = 2.545455 cm and the most demanding frequency that it needs to produce is 20kHz = 1.717cm

so 1.717 / 2.545455 = 0.67453559 times success digit

not even 1

As these figures drop, the diaphragm approaches the Because of Cone Break-up anomalies.

It is to be stressed that - the method used above cannot be linked directly  to loudspeakers performance. Since speed of sound in other materials are different from speed of sound in air. However it is a good starting reference.

Full time engineers will have the time to search and use the material's speed of sound / transmission of vibration to do comparison.

In actual fact this study is nearly exactly the one used by engineering community known as ka to one 1 comparison.

The condition of the true useful frequency of ka>1 or ka<1 and finally the ka=1 theory. Please note that these theory are devised form reverse engineering through practical measurements. Therefore they are near 100% accurate. Finally humans translation / interpretation of results is critical.

The use of ka>1 or ka<1 and finally the ka=1 theory is provided by many textbook started many years ago. It is unknown how many engineers really understand this capability and limitations. Most important where and how this formula comes from.

If one does not know where and how it came from then the use of this theory will not be effective. Saying this. The example given above is one form of the source of the development of the theory ka>1 or ka<1 and finally the ka=1.

We also know that the loudspeaker as a "medium" used to produce sound - INJECT acceleration and velocity from the cone / radiating surface into the air.

There are radiation impedance to concern.

We also know that it is due to these extreme requirement of rapid acceleration and velocity that the cone itself vibrate

But not to the source frequency (music source), instead it is the loudspeaker's own resonant frequency.

So these internal structural resonant frequency - BEND - the cone structure in which cause the - PROJECTING - sound to go hay-wire in directions, level, strength and phase.

Cone break-up performance is highly non-linear and non-predictable (in the normal useful context).

I think I will stop here. If you are still interested, please read more books or email me.

p.s. a device such as tweeter is "ALWAYS" working within the cone break-up anomaly. Remember this?

so 1.717 / 2.545455 = 0.67453559 times success digit

This is why when applying equalization (EQ) - it does NOT improve as wish. Because it is working in the non-linear range.