I think it depends on how much power required on the big driver. The sound wave perceived is based on frequency of the physical wave. Tweeter is smaller which means less force required means less current or voltage(power dependency on both, see RMS equations below) required to drive it to high frequency, so therefore easy to drive. The Subwoofer sized speakers, it better to have for low frequencies since it take alot of power in RMS to drive them.
Average electrical power
Electrical engineers often need to know the
power,
P, dissipated by an electrical resistance,
R. It is easy to do the calculation when there is a constant
current,
I, through the resistance. For a load of R ohms, power is defined simply as:
However, if the current is a time-varying function,
I(t), this formula must be extended to reflect the fact that the current (and thus the instantaneous power) is varying over time. If the function is periodic (such as household AC power), it is nonetheless still meaningful to talk about the
averagepower dissipated over time, which we calculate by taking the simple average of the power at each instant in the waveform or, equivalently, the squared current. That is,
| (where denotes the mean of a function) |
| (as R does not vary over time, it can be factored out) |
| (by definition of RMS) |
So, the RMS value,
IRMS, of the function
I(t) is the constant signal that yields the same power dissipation as the time-averaged power dissipation of the current
I(t).
We can also show by the same method that for a time-varying
voltage,
V(t), with RMS value
VRMS,
This equation can be used for any periodic
waveform, such as a
sinusoidal or
sawtooth waveform, allowing us to calculate the mean power delivered into a specified load.
By taking the square root of both these equations and multiplying them together, we get the equation
By the way, there is a equation relating frequency to power(we engineers know there are millions of power equations
, everything relates to energy or power since we deal with transfer of energy).
Parseval's theorem(power from frequency perspective):
In
physics and
engineering, Parseval's theorem is often written as:
where
represents the
continuous Fourier transform (in normalized, unitary form) of
x(
t) and
f represents the frequency component (not
angular frequency) of
x.
The interpretation of this form of the theorem is that the total
energy contained in a waveform
x(
t) summed across all of time
t is equal to the total energy of the waveform's Fourier Transform
X(
f) summed across all of its frequency components
f.
Basically what mcmalden is saying above is air friction area is proportional to the diaphram size since it moves back and forth through air, and more friction means more resistance force, means more force required to move the diaphram, means more power, which is proportional to force, means more current or voltage in RMS of power.
Conclusion. Its more efficient to have tweeter to be smaller sized because of the low power draw. I'm a EE, Fourier is our king(king of signals), not to menion Maxwell(electromagnetic guru that unified theory of light). Like Newton(the physics of above poster) is King of physics.