Q: “How does the size of the LF driver impact its frequency response? In other words, why does an 8″ driver go lower than a 6″ driver?”
A: This is a tricky question because the premise it is based on, depending upon how you interpret it, is not strictly true, or is at least potentially misleading. In fact a 6″ inch driver is capable of moving just as slowly as an 8″ inch driver so one could argue that it’s frequency response goes just as low. The previous statement would be true if we were discussing “frequency range,” but “frequency response” is a term that implies a relatively consistent amplitude, and that’s where a distinction needs to be made.
While the smaller speaker can move just as slow as a larger one it is not able to displace as much air while doing so. The greater volume of air moved by a larger speaker (at a given excursion) is a significant benefit when it comes to reproducing low frequency signals. To some extent this touches on the relationship between wavelength and frequency. But even at higher frequencies larger drivers potentially can have more output. The problem is that their mass (and corresponding inertia) prevents them from being able to move as fast as smaller drivers, thus they don’t reproduce high frequency signals very well (there are other factors, see below).
Getting back to how this applies to frequency response one must remember that we are concerned with relative amplitude levels. If we set a standard that we’re going to measure the frequency range of a loudspeaker at 110 db SPL, then any frequency falling significantly below that level (3 dB is a common cutoff point, but standards vary) cannot be considered part of the usable frequency response. All other things being equal an 8″ driver is going to be able to go a little further down before its output hits that -3 dB point than a 6″ driver, which purely boils down to how much air is being moved.
It’s important to note that these factors are dramatically effected by cabinet size and style, not to mention other differences in loudspeaker construction. It’s not safe to assume that all larger speakers will be more efficient at lower frequencies than smaller speakers.
Another aspect of this worth mentioning, though it wasn’t the crux of the question, is how high frequencies are effected by speaker size. We’ve already mentioned that due to mass higher frequencies will tend to be attenuated by larger (heavier) speakers. Another characteristic is that once the wavelength of the sound gets smaller than the diameter of the speaker cone the device will begin to become very directional. This is a phenomenon known as beaming.