Frequency response of a speaker cabinet on the rear axis



Last updated: April 25, 2018

Approximation of the frequency response of a speaker cabinet on the rear axis with a first-order low-pass filter.

In Rear Wall Reflection Simulator and Room Boundary Simulator I've used a first-order low-pass filter to calculate the frequency response behind the speaker cabinet. The cutoff frequency of the low-pass filter is shifted according to the baffle width. Of course, there is an obvious question: what is the validity of this simple calculation?

So I compared my rear-axis frequency response calculations with some measurements. These rear response graphs are normalized to the (front) on-axis response (in other words you can see the difference between the on-axis response and the rear radiation in dB).

Before I show the results I had to make some additional remarks:

The first measured curve is exported from the polar charts of a pro PA speaker (JBL AC2212-95). The speaker has a 12" woofer and the width of the cabinet is 355 mm. Unfortunately, there is no measured data below 200 Hz.


Normalized rear axis frequency resoponse of a 355mm wide PA speaker, simulation and measurement


The second one is an impulse response measurement of a small, 9 cm wide and 16 cm tall "multimedia" speaker. I've set the gate time to 8 msec, and the microphone distance from the baffle is 45 cm. (In the impulse response the first 8 msec is reflection free, this gives a 125 Hz low frequency limit.)


Normalized rear axis frequency resoponse of a 90mm wide speaker, simulation and measurement


As can be seen on the graphs the first-order low-pass filter approximation gives acceptable results. The maximum error is +- 2 dB between 0 dB and -15 dB, and only becomes larger where the response falls below -15 dB. The cutoff frequency of the low-pass filter can be shifted down or up according to the baffle width. If we need a more accurate calculation, then the geometric theory of diffraction, or modeling true wave propagation is a better choice.

Csaba Horvath

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