# Frequency response of a speaker cabinet on the rear axis

*April 25, 2018*

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

In Room Boundary Simulator the frequency response behind the speaker cabinet is simulated with a first-order low-pass filter. The cutoff frequency of the low-pass filter is shifted according to the baffle width.

This article compares the low-pass filter simulation with measurements. Rear response curves are normalized to the on-axis response (in other words we can see the difference between the frontal on-axis response and the rear radiation in dB).

Before showing the results some additional remarks:

- In the far field, the frequency response of a speaker behind the cabinet varies according to the angle of the measurement axis.
- In the near field, the frequency response behind the speaker cabinet is also a function of distance.
- On polar graphs of speaker cabinets the minimum of rear radiation (where the frequency response has the steepest slope) is on the 150 degree axis and not on the 180 degree rear axis.

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.

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.)

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 wave propagation is a better choice.

*Csaba Horváth*

See also:

Room Boundary Simulator

Measuring the sound radiation of speaker cabinet walls