Driver TS Parameters: Fs (Free Air Resonance)

The loudspeaker’s resonant frequency (often listed as Fs on spec sheets) is the frequency at which the driver’s cone and voice coil will tend to move easily. You’ve probably seen footage on TV of a bridge in the US wobbling around and tearing itself apart due to the wind causing the bridge to move at its resonant frequency – in case you haven’t, take a look here: http://www.youtube.com/watch?v=j-zczJXSxnw

The resonant frequency is influenced by the weight of the cone and voice coil (sometimes referred to as the moving mass) and the stiffness of the parts that return the cone to it’s central natural rest position. If you were to apply a sine wave signal to the speaker outside of a cabinet,  the speaker cone’s movement back and forth from rest position (known as excursion) will be significantly more at the resonant frequency than at higher frequencies.

Just as in the instance of the bridge being ripped apart at it’s resonant frequency, care has to be taken to avoid damaging your speaker. We wont get into the finer points of this here, but it’s something to be aware of, and you should be aware that many speaker designs recommend the use of a High Pass Filter, typically a little lower than the resonant frequency of the driver being used. Cabinet design can influence the recommended HPF, as for example in Bass Reflex Designs, the tuning of the reflex port reduces cone excursion at the resonant frequency, but can have the side effect of allowing increased excursion below the resonant frequency. The purpose of the HPF is to keep the driver operating within a frequency range that does not allow excessive excursion – without the HPF it is possible to damage your speakers through excursion without exceeding the power handling capacity of the speaker. However, if you set the HPF incorrectly, it is possible to reduce excursion too much, and since most woofers rely on the movement of the cone to push air through the voice coil vents, you do need to maintain excursion to keep air moving.

Its generally a safe bet for most designs to assume your driver wont be able to effectively product frequencies below it’s resonant frequency, and from a simplistic point of view, using a HPF just above the driver’s resonant frequency is a good way to stop your drivers being ripped apart from over-excursion.

A driver with a resonant frequency of say 50Hz will not be effective at sub-bass in the 30Hz region, so would be a poor choice for this application. A driver with a resonant frequency of 30Hz would probably work well from 33 Hz upwards, subject to an appropriate cabinet design, so could be used for sub-bass. Certain speaker designs (such as horn loaded speakers) work a little differently, and different results can be achieved.

However, if you are replacing an existing driver in a Ported Bass Reflex cabinet (one of the most common types), it’s generally a good idea to choose a replacement with a similar resonant frequency. The original speaker cabinet would have been tuned to match the driver, and putting in a significantly different driver will result in a mismatch, resulting in less than optimal performance, which in serious cases can result in premature failure of a driver due to over-excursion.

For serious sub-bass applications, the lower the Fs, the better. For mid-range, the resonant frequency of a cone driver is often irrelevant, as the operating frequency range will usually be significantly higher than the resonant frequency.

In compression drivers, the resonant frequency needs to be taken note of. Its normal to use compression drivers well above their resonant frequency, a typical 1″ exit compression driver would have a resonant frequency of 500-600Hz, and it’s normal to specify the minimum operating frequency an octave higher, which would be 1000-1200Hz. At it’s resonant frequency, the diaphragm on the compression driver will naturally move a lot more than normal, in a compression driver this can be catastrophic, as the metal dome on the compression driver can hit the front of the housing, and cause the diaphragm to shatter. Keeping an octave above the resonant frequency ensures the compression driver’s diaphragm stays within relatively low excursion limits.

It’s possible to damage diaphragms with bass and mid frequencies quite easily, it is for this reason that it’s common to put in a 1st order high pass filter ( a single capacitor) in series with a compression driver when it is used in an active system. This protects against accidental erroneous connection to the wrong amplifier, and it’s good practise to do this if your system has numerous connectors which look similar.

Once you start looking at the Thiele Small Parameters, you will start to become aware that speaker parameters all interact.  The formula which for F_s is as follows:

C_ms is a measure of the suspension (surround and spider) compliance. Compliance is the inverse of stiffness. High stiffness is low compliance. Low stiffness is high compliance. Stiffer suspension will make the resonant frequency higher, looser suspension will make the resonant frequency lower.

M_ms is the mass of the moving parts of the driver, including ‘air load’. A heavier cone will have a lower resonant frequency, and a lighter cone will have a higher resonant frequency.

You can read more about M_ms here: https://speakerwizard.co.uk/driver-ts-parameters-mmd-mms/.