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Re: On axis SPL -VS- acoustic power response

Posted by tomservo (M) on July 28, 2003 at 18:44:03

In Reply to: Re: On axis SPL -VS- acoustic power response posted by Bill Fitzmaurice on July 28, 2003 at 15:06:03:

Hi Bill

Back in the “old days” they were really concerned with efficiency so this frame of reference is how to see what’s going on.
ML’s math is for designing the efficient range of the horn only and not above that.
Voltage sensitivity alone also tells nothing of efficiency, the actual efficiency is the difference between the power dissipated in the coil and mechanical system compared to the energy radiated into the air.
For example, a horn is 50% efficient when the acoustic load raises the resistive part of the load impedance to about 2X Rdc. In this case, half the total input power is radiated as sound and the other half as heat.

Taking a physical model of a finite horn the size of the one you describe (except not folded and 1 flare rate) and the driver stuff, one gets a prediction like this. (This is making a few assumptions about the driver like its le etc)

A horn with a nominal “1 Watt” input (2Vrms with Rdc=4 Ohms) produced a response curve that was
+ - 3 dB from 115Hz to 4.2Khz
Was 105 dB avg from 120Hz to 3.5KHz

Looking at the impedance curve, one saw good acoustic loading from the low cutoff (a rear volume of 200 cu/in looked good) with an average efficiency of about 50% up to about 320Hz then falling to the driver Rdc+ a tad by 650Hz
This would be the efficient range of the horn, the one ML’s math is designing for.

Unlike the old days when tube amps were used, SS amps all have very low output impedance’s and so when the impedance falls on either side of the efficiency range, there can be some compensation because the lower load impedance draws more current (more power). Back then the impedance falling meant less power not more. So far as actual efficiency goes, the horn is done by about 650Hz.

Given a 22 By 22 inch mouth and assuming a simple exponential horn, one see’s a reason for the extended response when the polar response is examined.

At low frequencies, this horn is too small to have any directivity but by the time one reaches about 800Hz, its radiation pattern has fallen from a full spherical down to about a 160 degree cone.
By the time one gets to 4Khz, one has about a 60 degree radiation cone (where level has fallen -6dB from on axis). This means that the energy is radiated into a progressively smaller spherical area at a rate which very closely compensates the drivers falling acoustic power above about 500-600Hz
I don’t know the specifics of your box but if it had two or more horn paths (like a “W”bin) it would be possible to get more directivity than this simple shape.
Also, two “unknowns” were included, the series L and front volume both effect the horn response.
I assumed a low inductance of .5 Mhy (Rdc =4) and it was necessary to reduce the front volume down to about .2 Liters or less to go up that high (4-5KHz).

I don’t know how close this to what you measure but it shows the effect I was talking about.
Cheers,

Tom

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