Several people have asked for the code that I used in a previous post to calculate and plot first-reflection delay times as a function of listener- and loudspeaker-placement. So here it is.
Running the script below will produce pdf or postscript graphics output that looks like this:
I’ve been doing some work on determining the best toe-in angle for a dipole loudspeaker. The mathematical details are in this draft manuscript, but here is a brief summary.
Attenuating Lateral Room Reflections
By toeing-in a dipole one can selectively attenuate various room reflections by placing them at or near a dipole null (i.e. 90° off-axis). Shown here are two scenarios for the first lateral reflection paths in a room, with the polar response of an ideal dipole superimposed. Only the dipole orientation changes, the reflection paths are the same in both cases:
The first case is typical; the side-wall reflection is severely attenuated (about 30dB) since it is radiated near the dipole null. The front reflection is helped a bit, but it’s only down 3dB (plus about 4dB due to path length). In practice a mirror placed at the side wall reflection point will show an image of the loudspeaker on-edge. Continue reading
When loudspeakers are placed close to walls, the delay between the direct and reflected sound waves affects not only the perceived timbre (due to room gain and comb filtering) but also the degree to which believable phantom stereo images are created. If reflected sound waves arrive too soon after the direct sound, they generate spurious directional cues that spoil the stereo-imaging magician’s trick.
Some people go to great lengths to absorb room reflections with acoustic absorbers and diffusers, but the evidence  suggests this probably isn’t a good idea. These products have inherently uneven frequency response; their presence can drastically alter the timbre of the reflected sound, and it’s harder for the ear/brain to ignore reflections if their spectral content is different from the direct sound. Continue reading
When we combine the outputs of two loudspeaker drivers with a crossover, we usually want the drivers’ outputs to add in-phase. Otherwise the summed frequency response gets wobbly, as does the polar response, thanks to destructive interference. Even with an even-order crossover designed to have its outputs in-phase, there’s usually some confounding factor to mess things up: physical offsets of the drivers, and/or phase shifts introduced by equalization, the acoustic response of the baffle, and the high-pass characteristic of the drivers themselves.
The remedy here is to delay the signal to one of the drivers, bringing them into alignment at the crossover frequency (and hopefully out to an octave or so on either side). In the analog world this can be done by exploiting the group delay of an all-pass filter. With a digital crossover it’s easier: we just hold back the signal for as many samples as needed.
But how to set the right amount of delay? Here’s the standard trick: Continue reading