prk@charm.UUCP (Paul Kolodner) (05/08/85)
A recent posting asked the following question, in paraphrase: How come,
prk@charm.UUCP (Paul Kolodner) (05/08/85)
Phase distortion in tweeters - reply net.audio (Please excuse previous fragment - I was strangled by my editor.) A recent posting asked the musical question: how come movements of the head don't introduce phase distortion by changing the phase of the sound waves coming from the tweeter with respect to those coming from the woofer? Well, the answer to this question resembles the notion of a coherence angle in optics. If you have two sources of radiation at a distance d, then the question is, at what angle from the center line do the phases of the waves coming from the separate sources differ by an unacceptable angle, say, pi/4? Answer (from high-school geometry): sine of angle equals wavelength divided by 8d. For wavelength = 6 cm and d = 30 cm, angle = 1.4 degrees, rather small. However, there are some wrinkles which change things. First, the waves from the woofer have rather long wavelength; their phase is thus roughly constant everywhere in the coherence angle, effectively increasing it by a factor 2 to 2.8 degrees (still small). More to the point, in my opinion, the phase relationship between the fundamentals from the woofer and their high harmaonics from the tweeter is not that important. What's probably more perceptible is the phase relationships among different high notes and between different low notes. Now, the coherence angle is much larger, since we're considering waves which emanate from different sides of the same radiator. So, for a 6kHz tone from a 6 cm tweeter, the coherence angle is 15 degrees - quite wide, actually, unless you have a very wide head ! The angle is even larger in the bass. I think that's a good first-order answer to the question: small source equals wide coherence angle.