In his paper "Development of a Compact Diple Loudspeaker", Siegfired Linkwitz spelled out the concept of an idealized dipole as a positive and a negative acoustic source spaced at a distance D from each other. The trace below shows graphically the first dipole reinforcement peak followed by the first cancellation dip at twice the frequency. The peaks are at odd multiples of the reinforcement peak, the nulls are at even multiples of the reinforcement peak.
The slope from the first cancellation peak down is 6dB/octave.
This perfect dipole behavior is not of this world however in a real application. Other than the slope, the first couple of peaks nothing much is seen of this simple dipole model in real life. Further modelling is required to predict the behavior of a driver on a dipole baffle. The next plot shows what happens if the same model is applied to a RD75 on a baffle. The RD75 is a linesource with a 2" wide ribbon. The next trace shows the dipole model applied to the RD75 as a 2" wide planar with the ribbon not moving at the ends..
The slope, peaks and dips are the same as in the simple dipole model but the magnitude response is more realistic in the above case. The next plot shows one more variable thrown in the equation. Observe how the reinforcement peak is at the same location but the two dips are shifted down in frequency. The simulation below does not take into account the response of the driver itself nor any diffraction generated by the driver/baffle combination.
Although the above simulation is still not a perfect match for the measurements below with respect to magnitude, observe that the dips and peaks do occur in the right locations. The traces below are the result of measurements done in a large gym at different distances, the responses were normalised for same SPL in order to facilitate comparisons. There are some frequency fluctuations in the locatoin of the peaks and dips. More on this later. To be complete, the above simulations (2 and 3 parameters) were performed on a one-sided baffle with the same width as the one measured in the gym. According to the simple Linkwitz dipole model there should be a dip at 1500 Hz since it is an oven multiple of the basic reinforcment peak at 250 Hz. The enhanced simulation for a real linesource reveals a peak at this location, more or less confirmed by measurement. The traces in the measurement were 1/3rd octave smoothed to easier spot the trends.
Copyright (c) 1997-98, by Rudi A. Blondia, ALL RIGHTS RESERVED. Last update: March 17, 1998.