LOUDSPEAKER ENCLOSURES
217 sion of the If the behind the loudspeaker is less than
about the reactance is negative. If that dimension is greater than the reactance is usually if is absorbing material in the so that the loading on the back side of the loudspeaker is approxi- mately that for an infinite baffle.
MEDIUM-SIZED BOX. For those frequencies where the wavelength of sound is greater than eight times the smallest dimension of the box
<
for the box of Fig. the mechanical reactance presented t othe rear side of the loudspeaker is a series mass and
is the acoustic compliance of the box in meterss per newton and
is the acoustic mass in kilograms of the air load on the rear side of the dia- phragm due t o the box; and where
= volume of box in cubic meters. The volume of the loudspeaker should be subtracted from the actual volume of the box in order t o obtain this number. T o a first approximation, the volume of the speaker in meters3 equals 0.4 the fourth power of the ad-
vertised diameter in meters.
= 1.4 for air for adiabatic compressions.
= atmospheric pressure in newtons per square meter (about on normal days).
a a = if the loudspeaker is not circular.
B = a constant, given in Fig. 8.6, which is dependent upon the ratio of the effective area of the loudspeaker diaphragm t o the area L2 of the side of the box in which i t is mounted.
As an example, assume t h a t the depth of the box is 1 ft. Then, since Eq. (8.6) is restricted to the frequency region where
>
the maximum frequency for it is 140 cps.LARGE-SIZED BOX. If the box is large so that its smallest dimension is
greater than one-eighth wavelength, and if i t is unlined, the mechanical reactance is determined from Fig. 8.7.
Impedance o j with Absorptive Lining. The type of reactance function shown in Fig. 8.7 is not particularly because of the very
A t cps, a 72°F is 13.5 at 500 c p s , 27 i n . ; at 2000
L O U D S P E A K E R E N C L O S U R E S [Chap.
0.01 0.04 0.1 0.4 1
8.6. End-correction factor B for the reactance term of the impedance a t the rear side of the loudspeaker diaphragm mounted in a box of the type shown in Fig. 8.2.
The acoustic reactance of box on the diaphragm is given by =
+
For a noncircular diaphragm of area =Square root of piston area per unit wave length
FIG. 8.7. Specific acoustic reactance of a closed box L L with a diaphragm
of area a t center of L L face. of the first normal mode of vibration occurs when = that is, it occurs a t = for = 16;
for = 9; a t 0.5 for
-
4; and a t = 1 for = 1.Part 219
high value reaches a t the first normal mode of (reso- nance) for the box, which occurs when the depth of the box equals half wavelength. A high reactance reduces the radiated to a very small value. To reduce the magnitude of a t the first normal mode of vibration, an acoustical lining is placed in the box. This lining should be highly absorptive a t the frequency of mode of vibration and a t all higher frequencies. For normal-sized boxes, a satisfactory lining is a 1-in.-thick layer of bonded mineral wool, bonded Fiberglas, bonded hair felt, Cellufoam (bonded wood fibers), etc. For small cabinets, where the largest dimension is less than 18 in., a layer of absorbing material may be satisfactory.
At low frequencies, where the of the lining is less than 0.05 wavelength, the impedance of the box presented t o the rear side of the diaphragm equals
where is given in Eqs. (8.6) t o (8.8) and
= = one-third of the total resistance of a layer of the acoustical material t h a t lines the box divided by the area of the acoustical material The units are mks acoustic ohms. The flow resistance equals the ratio of the pressure drop across the sample of the material to the linear air velocity through it. For lightweight materials the flow resistance is about 100
rayls for each inch of thickness. For dense materials likt P F Fiberglas board or duct liner, the flow
may be as high as 2000 mks rayls for each inch of thickness of the material. For example, if the flow resistance per inch material is 500 rayls, the thickness 3 in., and the are:
then = = 2500 mks acoustic ohms
It is assumed in writing this that the material doe: not occupy more than 10 per cent of the volume of the box. = volume of the box in cubic meters including the volume of
acoustical lining material.
= volume of the acoustical lining material in cubic meters. Graphs of (8.10) are given in Fig 8.8.
At all where absorption of the lining is higl
(say, greater of the presented to the
side the will be the same as that presented to a piston in
Tables and graphs of absorption for materials arc given Chap. 10.
L O U D S P E A K E R E N C L O S I J R E S [Chap. 8
infinite baffle radiating into free space, so t h a t found from Fig. 5.3 or Eqs. and (8.3).
Acoustical material may also be used t o enlarge effectively the volume of enclosed air. Gaseous compressions in a sound wave are normally adiabatic. If the air space is completely filled with a soft, lightweight
material such as kapok or Cellufoam (foamed wood fibers), the com- pressions become isothermal. This t h a t speed of sound decreases from = 344.8 t o = Reference t o Fig. 8.7 t h a t this lowers the reactance a t low frequencies just as does an
i n dimension L. This also that in (8.7) the is instead of 1.4.
M I X ]
One special type of with absorptive lining is in
Fig. Here, the is near the end of a rectangular
of length and of cross-sectional area equal t o the effective of the loudspeaker dia-
phragm. A glass fiber wedge whose length is is used t o terminate the box. The specific acoustic resistance and reactance (multiplied by for such a box with and without the wedge are given in Fig. 8.10.
Three things of importance are ob- served about the impedance: (1) for a given volume of box, a t low frequencies, the reactance smaller than t h a t for t h e box of Fig. 8.2; (2) a t high frequencies, the box resonances (normal
minimizing the shift of resonance frequency
t h a t approaches . . and in a closed-box baffle.
approaches zero; and (3) between these
frequency regions [that is, 0.2
<
<
the reactance positive.FIG. 8.10. Normalized specific acoustic impedance of tube of length L with absorbing
wedge mounted in end. t h e wedge, Rss = 0.
of
Box
Compliance on Resonance Frequency. Let us analyze the effect of the closed-box baffle on the lowest resonance frequency of a direct-radiator loudspeaker. For a loudspeaker mounted in anD . A . Dobson, master's thesis, Electrica
Department, Massachusetts of Technology, Cambridge, Mass. 1951.
E N C L O S U R E S [Chap. 8
baffle, the frequency for zero reactance is
where we have assumed t h a t the radiation reactance from each side of the diaphragm equals and t h a t =
From Fig. 8.4 we see that the resonance frequency for the loudspeaker in a closed-box baffle with a volume less than about 8 is