## Helmholtz Resonator This graph is the property of Ready Acoustics

A Helmholtz resonator is simply a box with a port on its front side to couple the enclosed volume of the airspace in the box to the air in the room. The depth of the enclosed airspace in the box behind the port and the width and depth of the port control the resonant frequency of the bass trap.
Another form of helmholtz resonator is created using perforated plywood - i.e. plywood with hundreds of holes in it. You see it in hardware stores holding up tools etc. If you place a panel of this over an air cavity like in a panel resonator not only do the little holes act like bottle necks the whole panel acts as a low frequency panel resonator! Standing waves occur at harmonics of the fundamental frequency - that is 2, 3, and 4 times the fundamental. Thus a room with an 2.45 meter ceiling has standing waves forming at 70 Hz (the fundamental frequency or first harmonic), 140 Hz (the second harmonic), 210 Hz (the third harmonic) and 280 Hz (the fourth harmonic).
Rooms with smaller dimensions often have standing waves or resonance build ups that are very noticeable causing coloration at around 200 Hz.

## Calculate Standing Waves for 3 Dimensions (L, W & H)

 Room dimension: Length: m Width: m Height: m Length Width Height fundamental frequency (fo) : Hz Hz Hz first harmonic : Hz Hz Hz second harmonic : Hz Hz Hz third harmonic : Hz Hz Hz
The formula for determining the fundamental frequency of a standing wave for a particular room dimension is:

fo = V / 2d

where:
fo = Fundamental frequency of the standing wave
V = Velocity of sound (344 meter per second)
d = Room dimension being considered in meter (length, width and height)
The formula for determining fres:

fres = c/2 * sqrt( (l/lx)^2 + (m/mx)^2 + (n/nx)^2 ), with l,m,n = 0,1,2...

c = 344 m

## Calculate Helmholtz-Resonator

Calculate Resonant Frequency, Bandwidth and Q from given Volume, Port- length and Width.

Height: Width: Depth: Calculated Volume
cm cm cm Liter
Port Length: Port Diameter: Calculated Port Area:
cm cm cm2
shorter port =
higher resonant frequency,
higher bandwidth
smaller portdia. =
lower resonant frequency,
lower bandwidth
less volume =
higher resonant frequency,
higher bandwidth
longer port =
lower resonant frequency,
lower bandwidth
bigger portdia. =
higher resonant frequency,
higher bandwidth
more volume =
lower resonant frequency,
lower bandwidth
Resonant frequency : Flow (f1) : Fhigh (f2) : Bandwidth :
Hz Hz Hz Hz

The internal damping of the resonator is thus determined by the quality, while the outside damping of the resonator is seized by the sound field (thus those effect actually which can be used) by the coupling relationship k:
 k = 5 x 10-13 x V x F x Q x f3 k = coupling relationship [ cm3/s3 ] V = volume of the resonator [ cm3 ] Q = quality F = factor, which depends on the arrangement of the resonator in the area (applies only to single resonator) f = frequency [ cycles per second ]

#### Room corner :

Usual values for k lie between 0.02 (for small increased heights) and 0.4 (for strong increased heights). Helmholtzresonatoren show largest effect thus in space corners. Calculations are based on the American Institute of Physics Handbook, 1957 McGRaw Hill, Inc.

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