10. Room Acoustics & Environment · Concept 10 of 13
Helmholtz Resonance
The deep hum a hollow container makes when air bounces in and out of its neck, like blowing across a bottle.
Air in the neck (mass) bounces on the trapped cavity air (spring), ringing at one resonant frequency f set by neck area A, cavity volume V and neck length L.
What it is
A trapped pocket of air that springs back and forth through a narrow opening, ringing at one fixed low pitch.
Key facts
Speed of sound in air = 343 m/s at 20 degC (rises ~0.6 m/s per +1 degC)
Helmholtz formula: f = (c / 2*pi) * sqrt( A / (V * L_eff) )
Symbols: f = frequency (Hz), c = speed of sound (343 m/s), A = neck area (m^2), V = cavity volume (m^3), L_eff = effective neck length (m)
L_eff = real neck length + end correction; add ~0.85 * neck radius per open end
Bigger cavity volume V = LOWER pitch (f scales as 1/sqrt(V)); bigger neck area A = higher pitch
A 330 ml beer bottle hoots ~100-185 Hz depending on how full it is
Ported (bass-reflex) sub tuning Fb typically ~30-45 Hz for live PA subs; at Fb the cone barely moves, the port does the work
Below Fb a ported box unloads and drops ~24 dB/octave (vs ~12 dB/oct sealed)
Doubling distance from a point source = -6 dB SPL; half the power = -3 dB; 10x power = +10 dB (~2x as loud)
Resonance depends only on V, A and L_eff (not shape); a Helmholtz absorber has Q ~5-15, a narrow notch that soaks one room mode
How it works
Air sealed in a cavity acts like a spring (squash it, it pushes back).
The slug of air in the neck acts like a mass sitting on that spring.
Push air in, spring compresses; it shoves the slug back out, then sucks it in again.
That spring-mass bounce repeats at one natural frequency f set by V, A and L_eff.
Blowing across the neck feeds energy in and the system rings at that pitch.
Build the cavity to your target Hz and it either RADIATES (sub port) or ABSORBS (bass trap) that note.
Real examples
Blowing across a beer bottle: ~150 Hz hoot, drops in pitch as you drink it (bigger air volume V).
A ported subwoofer cabinet: the port + box air resonate to extend bass down to ~35 Hz.
Guitar/violin body: the f-holes + soundbox form a Helmholtz resonator boosting low strings.
A slotted/perforated bass trap on a venue wall tuned to kill a 60 Hz room boom.
Wind buffeting one open car window at speed: that thumping pressure throb is Helmholtz.
How it helps in live sound
Know your subs' port tuning (Fb): high-passing at or just above Fb protects cones from over-excursion below tuning.
Never run a ported sub hard with NO high-pass; below Fb the cone flaps unloaded and can bottom out.
If a venue has one stubborn boomy note (e.g. 80 Hz), a tuned Helmholtz trap kills it without deadening the whole room.
Blocked or whistling sub ports change Fb and the bass response; check ports are clear before doors.
Use a parametric EQ notch (narrow Q ~5-10) at the room's resonant mode as a quick fix when you cannot place traps.
Measure the room mode first (RTA/REW sweep) so you build/EQ the trap at the EXACT Hz, not a guess.
Everyday analogy
It's a kid on a swing: the air in the bottle's belly is the springy seat and the air in the neck is the kid bouncing, and they only swing comfortably at one natural rhythm.
Watch out
Myth: a bigger bottle/box always sounds higher. Reverse: bigger cavity volume V LOWERS the pitch (f goes as 1/sqrt(V)), it's the neck size and air volume, not the container's looks.
Fun fact
The ocean roar you hear in a seashell is Helmholtz resonance: the shell's cavity picks out and amplifies a band of the ambient room noise around it, not the sea.
Key takeaways
Trapped air = spring, neck air = mass; together they ring at ONE low pitch.
f = (c/2pi)*sqrt(A/(V*L_eff)) - bigger V means lower note.
Sub PORTS use it to make bass; bass TRAPS use it to eat one note.
Always high-pass a ported sub at or just above its tuning (Fb).
Independent of shape: only volume, neck area and neck length matter.