Larger hole == higher resonance; smaller hole == lower
resonance frequency.
Diffraction effects might have more influence on HF
performance -- dunno.
Mike, I don't have the equations in front of me ....Anybody
know the equation?
My advice is to not mess with the hole in the front cavity.
The properties of the acoustic circuit in front of the
diaphragm is used to control the highest resonance of the
system -- that betwen the diaphragm and the cavity. The main
control is by use of acoustic resistance to damp the
resonance.
The equations are:
rho=density of air a = radius of hole
w-radian frequency u=coeff. of viscosity
c=velocity of sound gamma=ratio of specific heats ~1.4
V=volume of the cavity Po=resting pressure of air ~ 10^5
Newtons/m^2
acoustic mass of the hole ~ (rho/pi*a^2)*[t+1.7a]
acoustic resistance of the hole ~ (rho/pi*a^2)*SQRT(2*w*u)*
[t/a]
The entire front-side acoustic circuit is composed of series
elements ending in a compliance to ground that is the cavity
in front of the diaphragm providing pressure to the diaphragm.
The elements are, radiation resistance ~ 0.5*rho*c/a^2;
radiation mass ~ 0.2*rho/a
acoustic mass of the hole (above)
acoustic resistance of the hole (above)
acoustic compliance cavity load ~ V/(gamma*Po)
And lets not forget the acoustic resistance of the black
fuzzy stuff over the mic face.
So, three resistances and two masses all in series drive the
cavity load.
The damping that determins the upper resonance rise is
controlled by the total resistance in the circuit. Notice how
this element can be manipulated by diddling with the hole
radius. Ahhhh, the power of a^2 in the denominator!
You asked for equations, you got equations!
Dick Campbell
