To understand the complex thematic a loudspeaker on the floor can be minimally modelled as a mass-spring-damper 2 body system if we reduce the motions to one direction
View attachment 113115
where the complete loudspeaker (enclosure plus drivers) is mass m
a, the floor is mass m
m and the floor has its own stiffness km and damping and cm in relation to the earth with its "infinite" mass. The relative movement between loudspeaker and floor is coupled through the stiffness
ka and damping
ca of the connection between them (for example loudspeaker base or feet).
Excitation in this case been modelled as a sinusoidal force at the loudspeaker mass m
a and the vertical direction of x
a through the inertial reaction to the loudspeakers membranes motion (in this simplified teaching case of course also oscillating in vertical direction).
Ideally for our purposes we want the oscillation amplitude of both the loudspeaker mass x
a and floor mass x
m to be minimised, even more for higher frequencies as with increasing frequency the same amplitude creates a higher sound pressure.
Ideally our floor has very high stiffness and damping and thus isn't prone to high excitation, in this case we want as high stiffness
ka as possible for the loudspeaker to floor connection, which for the extreme case can be thought as just one combined mass and will minimise the loudspeaker oscillation amplitude too. Using in this case feet with high compliance (= low stiffness) is counterproductive as it will allow unnecessarily higher oscillations of the total loudspeaker (enclosure), especially till the resonance frequency of the coupling stiffness with the mass is reached, ω
0 = sqrt (
ka/m
a):
View attachment 113119
In above plot x axis is the
normalised excitation frequency ω/ω
0 and y axis is the normalised oscillation amplitude for different normalised damping factors ζ, as it can be seen above 1 (ω/ω0>1) the oscillation amplitude gets reduced but before its higher, especially close to the resonance frequency 1.0 (ω/ω0=1).
This result can be used also in the case our floor stiffness is not optimally high enough. In this case the first step is to reduce the loudspeaker oscillation itself as much as possible by increasing its mass, for example with heavy stone plates directly and stiffly connected to the loudspeakers base. Then we could ideally choose the stiffness and damping of the
connection of the plate to the floor by appropriate elastomers and/or mechanical spring/viscous dampers, we want a low enough stiffness that brings the resonance frequency of the coupling lower than the lowest frequency we will excite (for example lower than 20 Hz) and damping factor as high as possible, mind you that damping factor is often a compromise with low stiffness.
As it can be seen even for this significantly simplified case the problem is quite complex and in reality it gets more complex as we have (partially even coupled) vibrations in all 3 directions and not ideally stiff subsystems which show even their own (theoretically infinite) eigenmodes so its obvious that generic solutions like "audiophile feet" offered cannot be a guarantee for success. To sum it up our the solution can be very different depending on the stiffness of the floor.