Helmholtz Resonators

Herman von HELMHOLTZ

Resonator

http://en.wikipedia.org/wiki/Helmholtz_resonance

Helmholtz Resonance

A brass, spherical Helmholtz resonator based on Helmholtz's original design, from around 1890-1900.

Helmholtz resonance is the phenomenon of air resonance in a cavity. The name comes from a device created in the 1850s by Hermann von Helmholtz to show the height of the various tones. An example of Helmholtz resonance is the sound created when one blows across the top of an empty bottle.

Qualitative Explanation

When air is forced into a cavity, the pressure inside increases. Once the external force that forces the air into the cavity disappears, the higher-pressure air inside will flow out. However, this surge of air flowing out will tend to over-compensate, due to the inertia of the air in the neck, and the cavity will be left at a pressure slightly lower than the outside, causing air to be drawn back in. This process repeats with the magnitude of the pressure changes decreasing each time.

This effect is akin to that of a bungee-jumper bouncing on the end of a bungee rope, or a mass attached to a spring. Air trapped in the chamber acts as a spring. Changes in the dimensions of the chamber adjust the properties of the spring: a larger chamber would make for a weaker spring, and vice-versa.

The air in the port (the neck of the chamber) is the mass. Since it is in motion, it possesses some momentum. A longer port would make for a larger mass, and vice-versa. The diameter of the port is related to the mass of air and the volume of the chamber. A port that is too small in area for the chamber volume will "choke" the flow while one that is too large in area for the chamber volume tends to reduce the momentum of the air in the port.

Quantitative explanation

It can be shown[1] that the resonant angular frequency is given by:

\omega_{H} = \sqrt{\gamma\frac{A^2}{m} \frac{P_0}{V_0}} (rad/s) ,

where:

* ? (gamma) is the adiabatic index or ratio of specific heats. This value is usually 1.4 for air and diatomic gases.
* A is the cross-sectional area of the neck
* m is the mass in the neck
* P0 is the static pressure in the cavity
* V0 is the static volume of the cavity

For cylindrical or rectangular necks, we have

A = \frac{V_n}{L} ,

where:

* L is the length of the neck
* Vn is the volume of air in the neck

thus:

\omega_{H} = \sqrt{\gamma\frac{A}{m} \frac{V_n}{L} \frac{P_0}{V_0}}

By the definition of density: \frac{V_n}{m} = \frac{1}{\rho} , thus:

\omega_{H} = \sqrt{\gamma\frac{P_0}{\rho} \frac{A}{V_0 L}},

and

f_H = \frac{\omega_H}{2\pi} ,

where:

* fH is the resonant frequency (Hz)

The speed of sound in a gas is given by:

v = \sqrt{\gamma\frac{P_0}{\rho}} ,

thus, the frequency of the resonance is:

f_{H} = \frac{v}{2\pi}\sqrt{\frac{A}{V_0L}}

The length of the neck appears in the denominator because the inertia of the air in the neck is proportional to the length. The volume of the cavity appears in the denominator because the spring constant of the air in the cavity is inversely proportional to its volume. The area of the neck matters for two reasons. Increasing the area of the neck increases the inertia of the air proportionately, but also decreases the velocity at which the air rushes in and out.

Depending on the exact shape of the hole, the relative thickness of the sheet with respect to the size of the hole and the size of the cavity, this formula can have limitations. More sophisticated formula can still be derived analytically, with similar physical explanations (although some differences matter). See for example the book of F.Mechels [2]. Furthermore, if the mean flow over the resonator is high (Mach number above 0.3 typically), some corrections must be accounted for.

Applications

Helmholtz resonance finds application in internal combustion engines (see airbox), subwoofers and acoustics. In stringed instruments, such as the guitar and violin, the resonance curve of the instrument has the Helmholtz resonance as one of its peaks, along with other peaks coming from resonances of the vibration of the wood. An ocarina is essentially a Helmholtz resonator where the area of the neck can be easily varied to produce different tones. The West African djembe has a relatively small neck area, giving it a deep bass tone. The djembe may have been used in West African drumming as long as 3,000 years ago, making it much older than our knowledge of the physics involved.

Helmholtz resonators are used in architectural acoustics to reduce undesirable low frequency sounds (standing waves etc.) by building a resonator tuned to the problem frequency thereby eliminating it.

Helmholtz resonators are also used to build acoustic liners, which aim at reducing the noise of aircraft engines for example. These acoustic liners are made of two components:

* a simple sheet of metal (or another material), perforated with little holes that can be regularly spaced or irregularly spaced, called resistive sheet,

* a series of so-called honeycomb cavities (holes with a honeycomb shape, but in fact only their volume matters).

Such acoustic liners are used in most today's aircraft engines. The perforated sheet is usually visible from inside or outside the airplane; the honeycomb is just under it. The thickness of the perforated sheet is of importance, as shown above. Sometimes, there are two layers of liners; they are then called "2-DOF liners", by opposition to the "single DOF liners" (DOF meaning Degree Of Freedom).

This effect could also be used to reduce drag on aircraft by 40%.[3]

http://physics.kenyon.edu/EarlyApparatus/Rudolf_Koenig_Apparatus/Helmholtz_Resonator/Helmholtz_Resonator.html

Patents

Novel Helmholtz Resonator
CN101435356

Abstract -- The invention relates to a novel Helmholtz resonator which is arranged on an automobile exhaust pipe. The resonator comprises a resonance box and a tuning pipe, wherein the resonance box is spanned on the exhaust pipe which passes through the resonance box, and the tuning pipe is arranged on the exhaust pipe in the box and is positioned wholly inside the resonance box. Compared with the prior art, the resonator has the advantages of low resonance frequency and great noise reduction. The resonator is suitable for the low frequency noise abatement for an automobile exhaust system.

SILENCER OF INTERNAL COMBUSTION ENGINE
JP2009036185

Abstract -- PROBLEM TO BE SOLVED: To provide a silencer of an internal combustion engine capable of suppressing the intake and exhaust noise of a plurality of frequencies by one resonator. ; SOLUTION: In the silencer of the internal combustion engine including a hollow part for facilitating a sound attenuation function by resonance wherein a space communicating with the inside of an intake and exhaust pipe of the internal combustion engine is formed, a volume variable means for enabling a volume in the hollow part to be variable is provided. The volume variable means varies the volume by a throttle opening or engine negative pressure. A resonator switch means for switching a side branch type resonator and a Helmholtz type resonator is provided. ; COPYRIGHT:

RESONATOR
JP2008309050

Abstract -- PROBLEM TO BE SOLVED: To reduce the cost of a resonator by making a main-volume chamber and a sub-volume chamber communicate to an intake air duct via a neck part. ; SOLUTION: The resonator 1 includes a resonator body part 11 provided with the main-volume chamber 12 communicating to the intake air duct 4 via the neck part 10, and a long and narrow sub-volume chamber 13 directly connected to the main-volume chamber 12, and has a function of a Helmholtz type resonator of which resonance frequency is determined according to volume of the resonator body part 11 which is sum of volume of the main-volume chamber 12 and volume of the sub-volume chamber 13, and a function of a side branch type resonator of which resonance frequency is determined according to length along a longitudinal direction of the sub-volume chamber 13 together. Consequently, the resonator 1 can get two resonance frequencies without complicating a structure of the resonator body part 11, and can reduce manufacturing cost in general.

Infrasonic Helmholtz resonator
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Abstract -- An infrasonic Helmholtz resonator capable of producing clean sinusoidal frequencies in the range of 6-14 Hz is described.

High intensity infrasonic tunable resonant acoustic test cell
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Abstract -- An apparatus and method are provided for high intensity acoustic test cells that employ the Helmholtz resonator principle, incorporating at least one moderately-sized volume or test cell that is tunable to a given infrasonic to low-sonic frequency and generates sound of high intensity with very pure sinusoidal waveforms in this test cell or volume, by varying the geometry of a port which is connected to the test volume and open to either atmosphere or a second or input volume and by introducing to the test volume or the input volume a driving acoustic signal at the given tuned frequency. The apparatus and method are used for testing or performing experiments on materials, structures, devices, products, biological entities or humans at high acoustic intensities and frequencies in the low-sonic to infrasonic ranges.

ACOUSTIC MATERIAL
JP2006337886

Abstract of JP 2006337886 (A)
PROBLEM TO BE SOLVED: To provide an acoustic material which has excellent sound absorbing performance, can be made thinner than before, and is suitably used for, specially, an air-conditioning duct of an automobile. ; SOLUTION: The acoustic material is made of a fiber body or foamed body laminated on a surface of a base material and has a Helmholtz resonator structure comprising a void space 23 recessed in the acoustic material from a laminated surface 21 of the base material and a through hole 24 formed to reach the void space from the opposite surface from the laminated surface. When the volume V1 of the void space portion, the volume V2 of the through hole portion, and the volume V3 of the remaining portion of the acoustic material are so related that V1/(V1+V2+V3)=0.2 to 0.6, the acoustic material has excellent sound absorbing performance and can be made thinner than before.

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SOUND REPRODUCTION DEVICE
JP10075494

Acoustic alarm employing a resonant cavity arrangement
GB2316784

Sound absorptive hollow core structural panel
US6021612

STANDING WAVE SPACER FOR INTERNAL COMBUSTION ENGINE
JP10008990

POLYGON SCANNER
JP9311286

LINT HANDLING SYSTEM
CA2174460

HELMHOLTZ RESONATOR LOUDSPEAKER
WO9631106

SILENCER
JP9212176

Adjustable silencer for air intake of vehicular combustion engine
FR2743848

SOUND ABSORBER
JP9198051

Arrangement for reducing tire/road noise
US5839761

MAGNETIC TAG EXECUTING ACOUSTIC OR MAGNETIC INQUIRY
JP8249431

System for absorption of air noise
DE19533623

SOUND ABSORBING MATERIAL
JP9062267

TELEVISION RECEIVER
JP8322095

Assembly for reducing tyre/road surface noise.
EP0680866

DAMPING DEVICE FOR THERMO-ACOUSTIC VIBRATION IN COMBUSTION CHAMBER
JP7293885

Engine enclosure air inlet/discharge sound attenuator
US5625172

Sound absorber for motor vehicles
US5681072

HELMHOLTZ HYDRAULIC PRESSURE PULSATION FILTER OF GAS SEALED TYPE
JP8240202

GAS-TURBINE ENGINE AFTERBURNER
RU2117806

Apparatus for acoustic noise reduction
US5508477

Sound absorption system for automobile
DE4446080

Structure of rear window shelf portion to partition vehicular passenger compartment...
US5498050

PRODUCTION OF SOUND ABSORBING MATERIAL
JP8166787

Dynamics free low emissions gas turbine combustor
US5644918

Vehicle with IC engine
DE4435296

Method and composite resonator for tuning an engine air induction system
US5572966

INTAKE STRUCTURE OF ENGINE
JP8093583

ADAPTIVE MANIFOLD TUNING
WO9511373

Rotary throat cutoff device and method for reducing centrifugal fan noise.
EP0638728

RESONATOR TYPE SOUND-ABSORBING BODY AND SOUND-ABSORBING CEILING
JP8013642

Vibration-insulating panel element
US5473125

MULTIBLADE BLOWER
JP7332284

Sound-proofed swimming pool
FR2718479

SILENCER FOR ATTENUATING DISCHARGE NOISES...
WO9419596

Quantitative determination of air present in refrigerant sample
US5524477

RESONATOR
JP7208287

VOLUMETER
JP7190834

PISTON POWER MACHINE OR WORKING MACHINE
JP6213072

HAND-HELD APPARATUS RADIATING SOUND
JP6223215

GAS TURBINE COMBUSTION DEVICE
JP7139738

SOUND FIELD ADJUSTING DEVICE
JP7160268

COMBUSTION CHAMBER OF GAS TURBINE
JP6221563

SPEAKER SYSTEM
JP6205491

SILENCER DEVICE FOR COMBUSTION ENGINE
JP6202673

VOLUMENOMETER
JP7083730

VOLUMENOMETER
JP7083729

VOLUMENOMETER
JP7083728

VOLUMENOMETER
JP7083727

Silencer arrangement for combustion engines.
EP0589516

Exhaust gas system of an internal combustion engine
DE4330129

Sound absorption method for motor vehicles.
EP0586831

SECONDARY BURNER
JP6094227

SPEAKER SYSTEM
JP7015783

Air intake device for an internal combustion engine.
EP0569714

A refrigeration compressor.
EP0561383

Piston-type engine with valve cover
DE4305281

Covering element.
EP0584442

Sandwich construction panel for acoustic insulation
FR2700179

Noise-attenuating internal combustion engine air intake system
US5424494

Sound-absorbing housing cladding for machine
DE4241515

Piezoelectric sound sources
US5386479

Low frequency sound generation system for use in vehicular passenger compartments
US5394478

SOUND VOLUME CONTROLLER FOR PIANO
JP6149232

Device for determining the volume of objects using a chamber with two resonators
US5385069

Earplug and hearing devices formed in-situ
US5333622

SPEAKER EQUIPMENT
JP6038290

Acoustic muffler for high volume fluid flow utilizing Heimholtz resonators
US5276291

Musical instrument incorporating a Helmholtz resonator
US5248846

Gas turbine combustor.
EP0576717

RECIPROCATING TYPE ELECTRIC RAZOR
JP6000261

Self-supporting wall with sound absorbing properties.
EP0518305

Guard-rail with sound absorbing properties.
EP0518304

CALIBRATION OF SEISMIC STREAMERS IN A HELMHOLZ RESONATOR
US5210718

AIR SUCTION DEVICE FOR INTERNAL COMBUSTION ENGINES
DE4215416

EXTENDED FREQUENCY RANGE HELMHOLTZ RESONATORS
WO9321625

NOISE REDUCTION DEVICE
JP5195746

Sound attenuator for low frequencies, in particular for air ducts in paper mills.
EP0495763

SOUND ABSORBING BODY
JP5158484

CVD FILM FORMING DEVICE
JP5117860

Silencer arrangement for internal combustion engines.
EP0481450

NOISE REDUCTION DEVICE
JP5059927

No title available
JP5294230

SILENCER FOR FAN OF HOVERCRAFT(R)
JP5016795

ACTIVE MUFFLING DEVICE
JP4350314

SPEAKER SYSTEM
JP4336795

Loudspeaker system.
EP0456416

SOUND ABSORBING PANEL
CA2040076

Exhaust system for small planing boat
US5234364

Method and means to adjust sound characteristics of club head upon impact with golf ball
US5064197

ACTIVE TYPE PULSATION PRESSURE ABSORBER
JP6026448

HELMHOLTZ RESONANCE TYPE WIDE BAND TRANSMITTER-RECEIVER
JP4278798

ROTARY TYPE ENCLOSED COMPRESSOR
JP4265490

Tubewave damper probe for seismic applications
US5171943

SPEAKER UNIT
JP4369996

METHOD AND DEVICE FOR REGENERATING SOOTY SMOKE FILTER IN DIESEL ENGINE
JP3242413

ROTARY COMPRESSOR
JP4159490

INTERNAL SIDEBRANCH RESONATOR
US5162621

INTAKE PIPE WITH INTAKE RESONATOR
JP4109071

METHOD AND APPARATUS FOR MONITORING AND CONTROLLING A HEAT GENERATOR
CA2020832

QUASI-OPTICAL GYROTRON HAVING A YOKE STRUCTURE...
US5134341

Quasi-optical gyrotron
US5052003

LASER PRINTER DEVICE
JP4000469

EXHAUST DEVICE FOR SMALL SPEEDBOAT
JP3295791

PULSE COMBUSTION APPARATUS
CA2013491

DIRECT RADIATION TYPE SPEAKER
JP3201796

Fan silencer apparatus
GB2237323

VARIABLE TENSION TRANSDUCER
JP2123900

Acoustic apparatus.
EP0361445

VOLUMETER
JP3108614

Acoustic apparatus
US4987601

ELECTRIC ACOUSTIC UNIT CONVERTER
JP2075299

NOISE-SUPPRESSING DEVICE
JP2161134

Keyboard instrument.
EP0347775

IC engine exhaust system - incorporates Helmholtz resonator
DE3916429

GAS LASER
JP2285686

GAS LASER DEVICE
JP2281676

GAS LASER DEVICE
JP2270384

Arrangement for diminishing the noise level within a motor car.
EP0342353

Acoustic apparatus
US5004066

Acoustic apparatus.
EP0336303

Acoustic Apparatus.
EP0334238

Method and apparatus of expanding acoustic reproduction range.
EP0334217

Acoustic apparatus
US5012890

Passive structural and aerodynamic control of compressor surge
US5199856

Damping device for air transmitted and rigid-body sound vibrations.
EP0337077

INTAKE DEVICE FOR ENGINE
JP2176113

METHOD AND APPARATUS FOR MONITORING AND CONTROLLING A HEAT GENERATOR
WO8906771

Sound insulation panel for preset frequency bands
IT1225514

Compressor noise attenuation using branch type resonator
US4927342

ACOUSTIC DEVICE
JP2113697

MEASURING APPARATUS OF INTERNAL VOLUME
JP2064418

ELECTRIC/ELECTRONIC MUSICAL INSTRUMENT
JP2041098

ELECTRIC/ELECTRONIC MUSICAL INSTRUMENT
JP2041097

PORTABLE ELECTRIC MUSICAL INSTRUMENT
JP2029795

PORTABLE MUSICAL INSTRUMENT
JP2029794

AUTOMATIC WASHER
JP2026598

ELECTRONIC MUSICAL INSTRUMENT
JP1319792

ELECTRONIC MUSICAL INSTRUMENT
JP1319791

ELECTRONIC MUSICAL INSTRUMENT
JP1319790

ACOUSTIC EQUIPMENT
JP1254098

ACOUSTIC EQUIPMENT
JP1254097

ACOUSTIC EQUIPMENT
JP1241297

ACOUSTIC EQUIPMENT
JP1241296

MAGNETIC RESONANCE IMAGING DEVICE
JP1201247

VOLUMETER
JP1184417

ACOUSTIC DEVICE
JP1302998

ACOUSTIC DEVICE
JP1302997

BODY RESONANCE INSTRUMENT
JP1144099

VOLUME MEASURING INSTRUMENT
JP1118722

PRINTER
JP63239076

A silencing ventilating device
EP0265000

Method and apparatus for nonintrusively determining mach number
US4829813

VOLUMETER
JP63298013

Acoustic inspection method
EP0242060

Sound attenuating box
US4787473

VOLUMETER
JP63113315

VOLUMETER
JP63044127

Method of mounting a piezoelectric helmholtz transducer on a printed circuit board
US4630342

ACOUSTIC DISPLACEMENT METER
JP62070705

Measure for reducing the sound emitted from railway rails
DE3532765

SILENCER DEVICE FOR INTERNAL COMBUSTION ENGINE
JP62038815

FLUID DRIVING APPARATUS
JP61265396

Heating boiler
DE3517859

Exhaust system for outboard motors
US4897060

SILENCER DEVICE OF ADAPTABLE TYPE
JP61129414

Infra-sonic intensification of glow bed
SE456524

Method and apparatus for acoustically measuring the volume of an object
US4640130

Sound probe
DE3439546

SOUND ABSORPTIVE STRUCTURAL BLOCK WITH SEQUENCED CAVITIES
CA1214396

Exhaust system for outboard motors
US4607723

INTERNAL COMBUSTION PISTON ENGINE USING AIR CHAMBER IN PISTON
CA1242121

SPEAKER DEVICE
JP61020490

Broadband matching network
US4644505

Low noise hand-held hairdryer
US4596921

Sound-absorbing building element
DE3412432

Sound attenuating ventilating box
NL8304487

Burner for the processes of the autogenous welding technique
DE3329937

PULSER BURNER
JP60038514

PULSATING COMBUSTION APPARATUS
JP60033408

GASEOUS COMPONENT DETECTOR
JP59212761

General purpose modular acoustic signal generator
US4602245

PIEZOELECTRIC TYPE LOW FREQUENCY TRANSDUCER
JP59190795

Method and apparatus for low frequency active attenuation
US4527282

APPARATUS FOR DETECTING GAS TEMPERATURE
JP59160730

Gas pressure regulator
GB2136095

BAR FOR A POWER CHAIN SAW
CA1173330

Passive acoustic absorber device also absorbing low frequencies
FR2540912

Vehicle roof liner.
EP0079253

INFRARED RAY DETECTOR
JP59054950

Low frequency muffler
US4501341

SOUND SUPPRESSOR LINER
CA1160850

CYLINDER BLOCK OF INTERNAL-COMBUSTION ENGINE
JP58107839

Directional microphone with high frequency selective acoustic lens
US4401859

Perforate tube muffler
US4371053

Electro-acoustic transducer
US4379212

Piezo-electric ringing transducer.
EP0025955

COMPACT EXHAUST SILENCER FOR DIESEL LOCOMOTIVES
CA1138780

Two stroke cycle engine with sustained power stroke
US4370959

Mufflers for percussive pneumatic machines
US4294330

ELECTRONIC AUDIO SIGNALLING DEVICE FOR TELEPHONES
CA1138137

SOUND-ATTENUATING MUFFLER FOR EXHAUST GASES
CA1123749

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