Helmholtz Resonator Calculator
Calculate resonance frequency for acoustic cavities and sound absorbers
Calculate Helmholtz Resonance
Internal volume of the resonating cavity
Cross-sectional area of the neck opening
Physical length of the neck/opening
Acoustic end correction for the opening (usually 0-1.5 × radius)
Speed of sound in air (default: 344 m/s at 20°C)
Resonance Results
Helmholtz formula: f = (c/2π) × √(A₀/(V × L₀))
Effective length: L₀ = L + ΔL = 0.0000 m
Parameters: V = 0.000e+0 m³, A₀ = 0.000e+0 m², c = 344 m/s
Example: Bottle Resonator
Wine Bottle Experiment
Bottle volume: 750 mL = 0.00075 m³
Neck diameter: 2 cm → Area = π × (0.01)² = 3.14 × 10⁻⁴ m²
Neck length: 5 cm = 0.05 m
Speed of sound: 344 m/s
Calculation
f = (344/2π) × √(3.14×10⁻⁴/(0.00075×0.05))
f = 54.7 × √(3.14×10⁻⁴/3.75×10⁻⁵)
f = 54.7 × √8.37 = 54.7 × 2.89
f ≈ 158 Hz
Try This!
Blow across the top of an empty bottle to hear this resonance frequency. Add water to change the volume and hear the pitch rise!
Common Applications
Musical Instruments
Guitars, ocarinas, wind instruments
Sound amplification and tone shaping
Sound Absorption
Concert halls, recording studios
Frequency-specific noise control
Automotive
Exhaust systems, mufflers
Engine noise reduction/tuning
Physics Principles
c: Speed of sound in medium
A₀: Cross-sectional area of neck
V: Volume of cavity
L₀: Effective length of neck
Design Tips
Larger cavity volume = lower frequency
Larger neck area = higher frequency
Longer neck = lower frequency
End correction ≈ 0.6 × radius for circular opening
Understanding Helmholtz Resonators
What is a Helmholtz Resonator?
A Helmholtz resonator is an acoustic device consisting of a cavity connected to the outside through a narrow neck or opening. It acts like a mass-spring system where the air in the neck acts as the mass and the air in the cavity acts as the spring.
How It Works
- •Pressure Oscillations: Sound waves enter through the neck
- •Air Movement: Air oscillates between cavity and environment
- •Resonance: Maximum response at specific frequency
Formula Derivation
From acoustic theory:
f = (c/2π) × √(A₀/(V × L₀))
Where:
• c = speed of sound (m/s)
• A₀ = neck cross-sectional area (m²)
• V = cavity volume (m³)
• L₀ = effective neck length (m)
End Correction
The end correction accounts for the fact that the acoustic length is slightly longer than the physical length due to the way sound waves propagate at the opening.
Real-World Examples
Bottles & Jars
When you blow across a bottle opening, you create a Helmholtz resonator. The pitch depends on the bottle's volume and neck dimensions.
Acoustic Treatment
Recording studios use perforated panels with cavities behind them to absorb specific frequencies and control room acoustics.
Vehicle Exhausts
Car exhaust systems use resonator chambers to reduce specific engine frequencies while maintaining performance.