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Understanding Key Loudspeaker Parameters(3): Resonant Frequency (fo)--The Heartbeat of a Loudspeaker
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posted by Vincent Zhang
Published by IWISTAO
Among all loudspeaker parameters, resonance frequency (fo) is one of the most fundamental. It defines how the mechanical and electrical parts of a speaker behave together at low frequencies and has a direct influence on bass performance, cabinet design, and overall tonal character.
This article explains what fo is, why it matters, how it’s measured, and how you can use it to predict a speaker’s behavior.
1. What Is Resonance Frequency (fo)?
The resonance frequency (often written as fo or Fs) is the frequency at which the speaker’s moving system—its cone, voice coil, surround, and spider—naturally vibrates with minimal external force.
In other words, fo is where the restoring force of the suspension equals the mass inertia of the moving assembly. At this point, the system stores and releases energy efficiently, resulting in maximum cone movement and a peak in impedance.
If you measure impedance versus frequency, you’ll see a large hump in the low-frequency region. The frequency at the top of that hump is the resonance frequency (fo).
2. Typical fo Values and What They Mean
| Speaker Type | Typical fo Range | Behavior |
|---|---|---|
| Subwoofer (large cone) | 18–40 Hz | Deep bass, slow transient response |
| Mid-woofer (6–8″) | 40–80 Hz | Balanced low end |
| Full-range driver | 60–120 Hz | Wideband response, limited deep bass |
| Tweeter | 800–2,000 Hz | High-frequency only, steep high-pass filter required |
In general:
- Larger cones → lower fo
- Heavier moving mass → lower fo
- Stiffer suspensions → higher fo
Thus, a low-frequency driver is designed with a heavy cone and compliant suspension to achieve a low fo for better bass reproduction.
3. The Physics Behind fo
The resonance frequency can be approximated by this formula:
fo = (1 / 2π) × √(K / Mms)Where:
- K = mechanical stiffness of the suspension system (N/m)
- Mms = total moving mass of the cone, voice coil, and air load (kg)
From this, it’s clear that:
- A heavier cone (larger Mms) → lower fo
- A softer suspension (smaller K) → lower fo
- A stiffer suspension (larger K) → higher fo
This balance determines how easily the diaphragm moves at low frequencies and how deep the bass can extend.
4. Why fo Matters
a. Bass Extension and Sound Character
A lower fo allows a driver to reproduce deeper bass frequencies before response rolls off. For example, a woofer with fo = 25 Hz can deliver powerful sub-bass, while one with fo = 70 Hz will sound tighter but less deep.
b. Enclosure Design
In loudspeaker design, fo interacts directly with the enclosure tuning frequency (fb). For sealed boxes, fo largely determines the system resonance (Fc). For vented boxes, fb is often tuned near or slightly below fo to achieve a flat or extended low-frequency response.
Accurate fo data is essential when calculating Vas, Qts, and designing a box using the Thiele–Small model.
c. System Matching
If the speaker’s fo is too high relative to the cabinet volume or crossover point, it can cause a bass gap or phase distortion in multi-way systems. Matching drivers with compatible resonance characteristics ensures smoother integration.
d. Diagnostics and Quality Control
Over time, speaker suspensions can stiffen or loosen, shifting fo upward or downward. Measuring fo periodically helps identify aging, mechanical fatigue, or suspension damage.
5. How to Measure fo
Method 1 – Impedance Sweep
- Connect the speaker to a measurement system (e.g., REW, DATS, CLIO).
- Perform an impedance sweep from 10 Hz–1 kHz.
- The frequency at which impedance reaches its maximum peak is fo.
Method 2 – Signal Generator and Multimeter
- Apply a low-level sine signal and vary frequency.
- Measure current through the speaker.
- The frequency where current is at its minimum corresponds to maximum impedance—that’s fo.
6. Real-World Example
| Driver Model | Diameter | Measured fo | Application |
|---|---|---|---|
| 12″ Subwoofer | 300 mm | 28 Hz | Deep bass, large sealed box |
| 6.5″ Mid-woofer | 165 mm | 55 Hz | Bookshelf speaker |
| 3″ Full-range | 76 mm | 85 Hz | Compact portable audio |
| 1″ Dome Tweeter | 25 mm | 1.2 kHz | High-frequency section only |
7. Lower fo Is Not Always Better
While a low resonance frequency suggests deeper bass, it’s not always the goal. Extremely low fo may result in sluggish transient response, lower efficiency, or larger required enclosures. Designers aim for an optimal fo that balances extension, control, and sensitivity.
Conclusion
The resonance frequency (fo) is the beating heart of a loudspeaker’s low-frequency behavior. It defines how easily the cone moves, how deep the bass extends, and how the system should be tuned. By understanding and measuring fo, engineers and enthusiasts can design and match speakers that deliver precise, powerful, and natural sound—without relying on guesswork.
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