Speaker Fs is an important parameter to know for speaker designers and speaker users. It is often quoted as part of the marketing material when purchasing a new speaker, but what does it mean?
Speaker Fs is the resonant frequency of a speaker in free air. Free air means that the speaker is not in an enclosure. It is the natural frequency of the speaker and is generally the lowest frequency at which the driver can be used.
Everything has a natural resonant frequency. This is the frequency at which an object or component, such as a speaker driver, will resonate at its highest amplitude when stimulated by a frequency or oscillation.
At first, it’s hard to grasp why this is significant, what it means and how it impacts us as speaker designers and speaker users in the real world.
In this article, I will cover the basic principles of Speaker Fs, including:
- What is speaker Fs?
- Why does speaker Fs matter?
- How do you measure speaker Fs?
What Is Speaker Fs?
Fs, which is called the Free Air Resonance of the speaker, is the resonant frequency of a speaker driver when in free air. [source]
Free air simply means the driver is not in an enclosure.
Everything has a resonant frequency. If you put any object into an environment and subject it to vibration, there will be a frequency where that object will naturally vibrate at a much higher amplitude.
The particular frequency that causes the most excitation is called the resonant frequency or natural frequency. [source]
If you want to hear the resonant frequency (natural frequency) of a speaker driver, simply tap the cone with your finger.
As Fs is the frequency at which the speaker driver wants to vibrate freely and will vibrate with minimum effort, as you excite the cone by tapping it with your finger, you are stimulating the resonant frequency.
As a general rule of thumb, the resonant frequency of a loudspeaker driver is the lowest frequency at which the driver can be used. [source]
Speaker Fs And Spider Stiffness
One of the key components of a speaker is the spider, also known as the suspension. I have covered what the spider does in a loudspeaker in greater depth in this article, “What Does The Spider Do In A Speaker? (Simple explanation)“
The main purpose of the speaker spider is to provide the main restoring force (i.e. compliance) for the motor system.
How stiff the spider is will determine Fs, the speaker resonance.
Speaker resonance, Fs, is a function of compliance and mass, and they are related by the following formula: [source]
Fs = [6.28(Cs x Md)1/2]-1
where;
- Fs = Resonant frequency
- Cs = Driver compliance
- Md = Total mass of the driver
The total mass of the driver includes the weight of the cone, voice coil, spider, surround, and free-air mass load.
Are Fs And F0 The Same Thing?
Like most things in the world of speaker design, Fs is also known by multiple terms. Fs and F0 are the same thing.
F0 can sometimes denote the natural frequency or first mode of oscillation of a component or part. This is the resonant frequency.
As a result, Fs and F0 can get used interchangeably, but mean the same thing.
To learn more about modes, check out this article, “How Do You Read A Modal Analysis Result? (Explained)“
Why Does Speaker Fs Matter?
Speaker manufacturers typically publish the speaker Fs as part of their marketing materials, but why do we need to know this? What can a speaker designer or speaker enthusiast do with this information?
There are a few key reasons speaker Fs is important:
1. Cabinet Design
Since there is a specific frequency that your speaker driver will easily resonate at, it is important to know this to ensure that your cabinet design does not excite your speaker’s resonant frequency.
If your enclosure excites this resonant frequency, you will get the effect of ringing.
2. Sound Reproduction
Fs can give us an indication of how well a speaker will reproduce sound, in particular frequency ranges.
For example, a speaker driver with a lower resonate frequency will generally be better at low-frequency sound reproduction. [source]
Of course, there are lots of parameters that make up the performance of a speaker, so this does not mean that one speaker is “better” than the other.
In theory, a speaker with a lower Fs will reproduce lower frequencies better than a speaker driver with a higher Fs.
3. Low-Frequency Roll-Off
Fs is where the frequency begins to roll off and is typically the lowest frequency at which the driver can be used.
Your speaker will be able to reproduce sound lower than the Fs value, but it is not optimal, so as a general rule, Fs is often taken as the lowest operational frequency.
4. Sealed Enclosures
The value of Fs can give you an indication of the type of enclosure that would work best with your speaker driver.
If your Fs is very high, you will not get much bass from a sealed enclosure because the trapped air inside the enclosure is acting like a spring. This change in air loading mass will increase the speaker drivers’ resonance.
Bass starts to roll off lower than the resonant frequency of a speaker driver. If your Fs is high, then you will not get a good bass extension.
Placing your speaker in a well-sized sealed enclosure increases the Fs, so to pick a good speaker for a sealed enclosure, a good rule of thumb is to pick one with a low starting Fs, ideally below 24Hz.
5. Ported Enclosure
Speakers with a higher Fs work better in ported enclosures. It can be good practice to place speaker drivers with a high Fs into a ported enclosure in my opinion, and tune to the Fs value.
There is some variation in this and part of a much wider topic, but knowing your speaker FS is important for cabinet tuning.
How Do You Measure Speaker Fs?
There are a few different approaches to measuring speaker Fs, but generally, you will need:
- Your speaker
- A signal source (i.e. your audio input)
- A power amplifier
- A resistor that is the same impedance as the speaker
- Digital multimeter
The following video does a fantastic job of explaining how to measure speaker free air resonance.
Final Thoughts
Speaker Fs is an important value to know for a variety of reasons. It can help with cabinet design, sound reproduction, low-frequency roll-off and speaker enclosure selection.
Knowing your speaker’s Fs will help you better understand how it will perform and what type of enclosure will work best.
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