Helmholtz resonator calculator

Lumped Helmholtz resonator; effective neck length already includes end corrections.

acoustics-helmholtz.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	frequencyHz
	99.6675
	79.734

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

resonance band upper99.67 Hz✓ passes

BASELINE INPUTS

soundSpeed343 m/sneckArea100 mm^2volume1 LeffectiveLength30 mm

CALCULATED

frequency99.668 Hz

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Helmholtz resonator
# Scope: Lumped Helmholtz resonator; effective neck length already includes end corrections.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

soundSpeed = 343 m/s
neckArea = 100 mm^2
volume = 1 L
effectiveLength = 30 mm

frequency := soundSpeed/(2*pi)*sqrt(neckArea/(volume*effectiveLength)) [Hz]

check resonance band upper: frequency <= 150 Hz

scenario alternative: soundSpeed = 274.4 m/s

Calculated from your source · not saved

Baseline · Baseline

resonance band upper99.67 Hz ✓ passes

alternative · alternative

resonance band upper79.73 Hz ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

frequency: frequency = soundSpeed/(2*pi)*sqrt(neckArea/(volume*effectiveLength)) [Hz]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

sound speed: 343 m/s
neck area: 100 mm^2
volume: 1 L
effective length: 30 mm

Calculated

frequency: 99.6675 Hz

Assumptions and limits

Lumped Helmholtz resonator; effective neck length already includes end corrections.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Helmholtz resonator. Inputs: cavity volume; neck geometry; end correction; sound speed. Outputs: resonant frequency estimate. Model scope: Small-signal vibration and declared sound-propagation conditions. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: cavity volume, neck geometry, end correction, sound speed
Outputs: resonant frequency estimate
Modes: calculate, compare, sweep
Drawing: Spectrum and vibration animation

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS