fs: free-air resonance

Every driver is a mass on a spring. The cone, voice coil and the air immediately touching them are the mass; the surround and spider are the spring. Left alone, that pair has one frequency at which it wants to move:

f_s = \frac{1}{2\pi\sqrt{M_{ms} C_{ms}}}

M_{ms} is the moving mass in kilograms and C_{ms} the suspension compliance in meters per newton. Compliance is the reciprocal of stiffness, so a softer suspension means a larger C_{ms} and a lower resonance.

What it tells you

fs is the floor of the driver's useful range, not of the system's. A box raises resonance, never lowers it, so a sealed enclosure's cutoff is always above fs. A vented box can produce output below fs, but that output comes from the port, not the cone.

Two drivers with the same fs can behave completely differently, because fs says nothing about how that resonance is damped. That is Qts, and the two are always read together.

Typical values

A 25 mm dome tweeter resonates somewhere between 500 and 1500 Hz. A 6-inch midbass is usually 35 to 55 Hz. A 12-inch subwoofer driver is often 18 to 30 Hz. Very low fs in a small cone is achieved with a heavy cone and a soft suspension, and it is paid for in efficiency; see Hofmann's Iron Law.

A caution about measurement

fs shifts. It falls as the suspension loosens with use, often by several hertz over the first few hours of playing, and it moves with temperature and with drive level. Manufacturer figures are usually measured on a broken-in sample at a low level. A driver straight from the box may measure several hertz high, and this is not a fault.