Twl, only first order filters are phase coherent, no exceptions. First order usually refers to the electrical filter, not the inherent slope of the driver's response. Therefore a first order filter consists of one reactive element, either an inductor or capacitor, in series or parallel with the load (the driver). And the phase shift caused by the reactive element varies with frequency, as a function of the ratio of reactive impedance to load impedance. In an "idealized" first order filter, there is a woofer inductor and a tweeter capacitor, each of which has a 45 degree phase shift at the crossover frequency, but in opposite directions. Over the rest of the frequency spectrum that each driver is intended to cover, the phase shift caused by the reactive elements is less than 45 degrees. Above the woofer's crossover frequency, and below the tweeter's crossover frequency, their phase shifts gradually approach 90 degrees, again in opposite directions.
Higher order filters add 90 degrees of phase shift per order. For example, a second order filter will have a 90 degree phase shift on both woofer and tweeter at the crossover frequency, approaching 180 degrees in each driver at the extremes. The two 90 degree phase shifts at the crossover frequency in opposite directions gives a net 180 degree phase shift between the drivers, meaning that if the drivers are wired in the same absolute phase, there will be a null at the crossover frequency. This then necessitates that the input to one of the drivers be run in inverted phase, meaning that throughout the entire range covered by the two drivers, they are operating in opposite phase. Talk about screwing up the integrity of the waveform!
Twl is right, there is no variation in the speed of sound relative to frequency. Each driver has a different "acoustical center", which is the point at which sound can be said to originate. It is not a physical property but an acoustical one, although a good approximation for any given driver is to use the point where the voice coil former meets the cone or dome.
Higher order filters add 90 degrees of phase shift per order. For example, a second order filter will have a 90 degree phase shift on both woofer and tweeter at the crossover frequency, approaching 180 degrees in each driver at the extremes. The two 90 degree phase shifts at the crossover frequency in opposite directions gives a net 180 degree phase shift between the drivers, meaning that if the drivers are wired in the same absolute phase, there will be a null at the crossover frequency. This then necessitates that the input to one of the drivers be run in inverted phase, meaning that throughout the entire range covered by the two drivers, they are operating in opposite phase. Talk about screwing up the integrity of the waveform!
Twl is right, there is no variation in the speed of sound relative to frequency. Each driver has a different "acoustical center", which is the point at which sound can be said to originate. It is not a physical property but an acoustical one, although a good approximation for any given driver is to use the point where the voice coil former meets the cone or dome.