7.21. Dual-concentric drive units

A difficulty with mounting a woofer and tweeter side by side or one above the other is that the path that the sound has to travel from each of the loudspeakers to a listener will be different in different parts of the listening room. Hence, in the vicinity of the crossover frequencies, cancellation of the sound will result at some parts of the room, and addition will occur at others.
To avoid this effect, the loudspeakers are sometimes mounted concentrically, i.e., the tweeter is placed behind and on the axis of the woofer (see Fig. 7.52). In this arrangement, the diaphragm of the woofer acts as a horn and the tweeter usually has a phase plug in front of it. Horn loudspeakers will be discussed in greater detail in Chapter 9.
Problem 7.1. A loudspeaker drive unit with a fiberglass cone has the Thiele-Small parameters: RE  = 5.6 Ω, QES = 0.46, QMS = 7.58, fS = 50 Hz, SD = 137 cm3, and VAS  = 19.5 L.
Calculate the box volume and port dimensions needed to give a Chebyshev frequency response with 0.01 dB ripple and a maximum sound pressure of SPL max = 100 dB SPL at 1 m. Show that to make the port volume ten times the volume displacement needed to produce 100 dB SPL, the optimum bore diameter is around 9 cm. Also, calculate the cut-off frequency.
image
Figure 7.52 Section view of a Blade UniQ two-way drive unit. The tweeter is located at the center of the woofer behind a “tangerine” phase plug and has its own independent voice coil. Note that the woofer diaphragm is driven half way along its radius to eliminate the first radial mode together with its odd-order harmonics. 
Courtesy of KEF.
Hint: Obtain QTS from Eq. (6.10). Obtain VAB and fB from Table 7.4. Calculate the maximum peak pressure and volume displacement required to produce that pressure using formulas from “Summary of bass-reflex design” on p. 334. Let the port volume be VP = 10V max and use Eqs. (7.97) and (7.96) to calculate the approximate length t and cross-sectional area SP respectively so that the diameter is dP=2SP/π image . Using a diameter of 9 cm, then calculate the exact length t from Eq. (7.98). Obtain the cut-off frequency f3dB from Table 7.4.
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