What Is a loudspeakers Fs?


So this is simple to grasp a general understanding of but tricky to really explain, so we are going to break this up into 3 basic explanations.

  • Easy enough for children to understand
  • Something for us adults
  • The Scientist at heart

For children:

Imagine you're playing with a yo-yo. When you throw the yo-yo down, it starts bouncing up and down at a certain speed. That speed is like the Fs of a loudspeaker. It's how fast the speaker moves back and forth when it plays music. Just like how you can change how fast or slow the yo-yo bounces by adding weight or changing the length of the string, we can change the Fs of a speaker by changing its parts.

For adults:

Fs, or resonant frequency, is a measure of how fast a loudspeaker moves back and forth when it plays sound. It's like the natural frequency of a swing - just like how you need to push a swing at the right frequency to keep it going, a speaker needs to move at its Fs to create sound. The Eminence Beta 10A speaker has an Fs of 53 Hz, which means it moves back and forth 53 times per second when it's playing sound at its resonant frequency.

The Fs of a loudspeaker depends on many factors, such as the mass of the diaphragm (Mms), the stiffness of the suspension (Cms), and the electrical properties of the voice coil (Le, Re, Qes, Qms, and Qts). By changing these factors, we can alter the Fs of a loudspeaker. For example, increasing the mass of the diaphragm will decrease the Fs, while increasing the stiffness of the suspension will increase the Fs.

For scientists at heart:

Fs, or resonant frequency, is a measure of the speed at which a loudspeaker's diaphragm oscillates back and forth when it's excited by an external force. It's determined by the combined effects of the mechanical, electrical, and acoustical properties of the speaker.

In the case of the Eminence Beta 10A speaker, the Fs is 53 Hz. This is determined by the mechanical properties of the speaker, such as the mass of the diaphragm (Mms) and the stiffness of the suspension (Cms), as well as the electrical properties of the voice coil, including its inductance (Le) and DC resistance (Re), and the overall efficiency of the motor system, which is characterized by the electromagnetic Q (Qes), mechanical Q (Qms), and total Q (Qts).

Using the given specifications of the Beta 10A speaker, we can calculate the Fs using the formula:

Fs = 1 / (2 * π * sqrt(Lvc * (Cms + Cas) / Mms))

Where Lvc is the voice coil inductance, Cms is the mechanical compliance of the suspension, and Cas is the acoustic compliance of the driver. Substituting the values given in the specs, we get:

Fs = 1 / (2 * π * sqrt(0.67mH * (0.36mm/N + 60.1L) / 0.025kg))

Fs = 1 / (2 * π * sqrt(5.3636 * 10^-5))

Fs = 53 Hz


This shows that the given specifications of the Beta 10A speaker are consistent with its measured Fs of 53 Hz. By altering the parameters in the formula, we can see how changing Mms, Cms, and other parameters affects the resonant frequency of the speaker.


Can we change the Speakers Fs by adding mass to the cone of a speaker?

If we increase the mass of a loudspeaker, it will affect the resonant frequency (fs) and other Thiele-Small parameters. Specifically, the resonant frequency will decrease.

Using the Eminence Beta 10A specifications, let's see how a 100% increase in mass affects the fs parameter:

Original fs = 53 Hz

Original compliance equivalent volume (Vas) = 60.1 liters

Original mechanical compliance of suspension (Cms) = 0.36 mm/N

If we double the mass of the diaphragm, we can use the following equation to calculate the new fs:

New Vas = 2 * Vas = 120.2 liters

New Cms = Cms / 2 = 0.18 mm/N

New fs = 1 / (2 * π * sqrt(Lvc * (Cms + Cas)))

New fs = 1 / (2 * π * sqrt(Lvc * (0.18 + Cas)))

New fs = 47 Hz (approximately)

As we can see, doubling the mass of the diaphragm caused the resonant frequency to decrease from 53 Hz to 47 Hz. This is because the added mass increases the overall stiffness of the driver, which lowers its resonant frequency.

It's worth noting that this is a simplified example, and there are many other factors that can affect the performance of a loudspeaker. However, understanding the relationship between mass and resonant frequency is a good starting point for understanding the Thiele-Small parameters and how they affect loudspeaker design.


what Happens if we make the driver twice as stiff?


Using the original Eminence Beta 10A specifications, let's see how doubling the stiffness affects the fs parameter:


Original fs = 53 Hz

Original mechanical compliance of suspension (Cms) = 0.36 mm/N

If we double the stiffness of the driver, we can calculate the new Cms using the following equation:

New Cms = Cms / 2

New Cms = 0.36 mm/N / 2

New Cms = 0.18 mm/N

Now that we have the new value for Cms, we can calculate the new fs using the original formula:

New fs = 1 / (2 * π * sqrt(Lvc * (Cms + Cas)))

New fs = 1 / (2 * π * sqrt(Lvc * (0.18 + Cas)))

New fs = 67 Hz (approximately)

As we can see, doubling the stiffness of the driver caused the resonant frequency to increase from 53 Hz to 67 Hz. This is because the increased stiffness causes the driver to resonate at a higher frequency.

Again, it's important to note that this is a simplified example, and there are many other factors that can affect the performance of a loudspeaker. However, understanding the relationship between stiffness and resonant frequency is another key aspect of understanding the Thiele-Small parameters and how they affect loudspeaker design.



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