Loudspeakers 68523.8 Diaphragm/Suspension Assembly ........................................................................
Assuming that the diaphragm behaves as a rigid piston and is mass controlled, the power
response is shown in Figure 23.7 where f 0 is the system fundamental resonant frequency.
Above this, the system is mass controlled and provides a level response up to ft ; this
corresponds toKa 2 (see Figure 23.3 ). Above this frequency the radiation resistance is
independent of frequency, and the response would fall at 12 dB/octave, but because of the
“ directivity ” effect, the sound fi eld is concentrated into a progressively narrower beam.
The maximum theoretical rate of rise due to this effect is 12 dB/octave, thus the on-axis
HF response should be fl at. In real life this is only approximated.
23.9 Diaphragm Size .....................................................................................................
It has been found experimentally that the effective area of the cone is its projected or base
area. This should not be confused with the advertised diameter of the loudspeaker, which
is anything from 25 to 50 mm greater than the effective cone diameter. In direct radiator
loudspeakers and at low frequencies, radiation resistance is proportional to the fourth
power of the radius (square of the area) and the mass reactance to the cube of the radius.
The resistance/reactance ratio (or power factor) of the radiation impedance is therefore
proportional to piston radius. Thus the electroacoustic effi ciency, other factors being
constant, increases with diaphragm area at low frequencies. For constant radiated power,
the piston displacement varies inversely with area, hence “ long throw ” type of small
diaphragm area loudspeakers. With fi xed amplitude, the radiated power is proportional
to the square of the area at a given frequency, or a frequency one octave lower may be
reproduced if the area is increased by a factor of four. The upper limit of diaphragm size
is set by increased weight per unit area required to give a suffi ciently rigid structure.
FrequencyPower 12 dB/octavefo ftFigure 23.7 : Power response of an infi nitely rigid piston.