Helmholtz resonance
Encyclopedia
Helmholtz resonance is the phenomenon of air resonance
in a cavity, such as when one blows across the top of an empty bottle. The name comes from a device created in the 1850s by Hermann von Helmholtz
, the "Helmholtz resonator", which he, the author of the classic study of acoustic science, used to identify the various frequencies
or musical pitches
present in music and other complex sounds.
inside increases. When the external force pushing the air into the cavity is removed, the higher-pressure air inside will flow out. 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.
The air in the port (the neck of the chamber) has 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.
(rad/s),
where:
For cylindrical or rectangular necks, we have
,
where:
thus:
By the definition of density
:
, thus:
,
and
,
where:
The speed of sound in a gas is given by:
,
thus, the frequency of the resonance is:
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 by F. Mechels. Furthermore, if the mean flow over the resonator is high (typically with a Mach number above 0.3), some corrections must be applied.
), 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 to accompany West African drumming as long as 3,000 years ago, making it much older than our knowledge of the physics involved.
The theory of Helmholtz resonators are used in motorcycle and car exhausts to alter the sound of the exhaust note and for differences in power delivery by adding chambers to the exhaust. Exhaust resonators also used to reduce potentially loud and obnoxious engine noise where the dimensions are calculated so that the waves reflected by the resonator help cancel out certain frequencies of sound in the exhaust.
In some twostroke engines, a Helmholtz resonator is used to remove the need for a reed valve
, which is a consumable component and therefore undesirable in engines with long running time. A similar effect is also used in the exhaust system of most twostroke engines, using a reflected pressure pulse to supercharge the cylinder (see Kadenacy effect
.)
Helmholtz resonators are used in architectural acoustics
to reduce undesirable low frequency sounds (standing wave
s, etc.) by building a resonator tuned to the problem frequency, thereby eliminating it.
Helmholtz resonators are also used to build acoustic liners for reducing the noise of aircraft engines, for example. These acoustic liners are made of two components:
Such acoustic liners are used in most of 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" (DOF meaning Degrees Of Freedom), as opposed to "single DOF liners".
This effect might also be used to reduce skin friction drag on aircraft wings by 40%.
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
in a cavity, such as when one blows across the top of an empty bottle. The name comes from a device created in the 1850s by Hermann von Helmholtz
Hermann von Helmholtz
Hermann Ludwig Ferdinand von Helmholtz was a German physician and physicist who made significant contributions to several widely varied areas of modern science...
, the "Helmholtz resonator", which he, the author of the classic study of acoustic science, used to identify the various frequencies
Audio frequency
An audio frequency or audible frequency is characterized as a periodic vibration whose frequency is audible to the average human...
or musical pitches
Pitch (music)
Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...
present in music and other complex sounds.
Qualitative explanation
When air is forced into a cavity, the pressurePressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
inside increases. When the external force pushing the air into the cavity is removed, the higher-pressure air inside will flow out. 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.
The air in the port (the neck of the chamber) has 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 that the resonant angular frequency is given by: (rad/s),where:
(gamma) is the adiabatic index or ratio of specific heats. This value is usually 1.4 for air and diatomic gasesDiatomicDiatomic molecules are molecules composed only of two atoms, of either the same or different chemical elements. The prefix di- means two in Greek. Common diatomic molecules are hydrogen , nitrogen , oxygen , and carbon monoxide . Seven elements exist in the diatomic state in the liquid and solid...
.- A is the cross-sectional area of the neck
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
,where:
- L is the length of the neck
-
is the volume of air in the neck
thus:
By the definition of density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
:
, thus: ,and
,where:
- fH is the resonant frequencyFrequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
(HzHertzThe hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
)
The speed of sound in a gas is given by:
,thus, the frequency of the resonance is:
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 by F. Mechels. Furthermore, if the mean flow over the resonator is high (typically with a Mach number above 0.3), some corrections must be applied.
Applications
Helmholtz resonance finds application in internal combustion engines (see airboxAirbox
Motorcyclists and car enthusiasts use the term airbox for what might more properly be described as an air intake chamber. Older engines drew air directly from the surroundings into each individual carburetor...
), subwoofers and acoustics
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of 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
Ocarina
The ocarina is an ancient flute-like wind instrument. Variations do exist, but a typical ocarina is an enclosed space with four to twelve finger holes and a mouthpiece that projects from the body...
is essentially a Helmholtz resonator where the area of the neck can be easily varied to produce different tones. The West African djembe
Djembe
A djembe also known as jembe, jenbe, djbobimbe, jymbe, yembe, or jimbay, or sanbanyi in Susu; is a skin-covered drum meant played with bare hands....
has a relatively small neck area, giving it a deep bass tone. The djembe may have been used to accompany West African drumming as long as 3,000 years ago, making it much older than our knowledge of the physics involved.
The theory of Helmholtz resonators are used in motorcycle and car exhausts to alter the sound of the exhaust note and for differences in power delivery by adding chambers to the exhaust. Exhaust resonators also used to reduce potentially loud and obnoxious engine noise where the dimensions are calculated so that the waves reflected by the resonator help cancel out certain frequencies of sound in the exhaust.
In some twostroke engines, a Helmholtz resonator is used to remove the need for a reed valve
Reed valve
Reed valves are a type of check valve which restrict the flow of fluids to a single direction, opening and closing under changing pressure on each face...
, which is a consumable component and therefore undesirable in engines with long running time. A similar effect is also used in the exhaust system of most twostroke engines, using a reflected pressure pulse to supercharge the cylinder (see Kadenacy effect
Kadenacy effect
The Kadenacy effect is an effect of pressure-waves in gases. It is named after Michel Kadenacy who obtained a French patent for an engine utilizing the effect in 1933. There are also European and US patents...
.)
Helmholtz resonators are used in architectural acoustics
Architectural acoustics
Architectural acoustics is the science of noise control within buildings. The first application of architectural acoustics was in the design of opera houses and then concert halls. More widely, noise suppression is critical in the design of multi-unit dwellings and business premises that generate...
to reduce undesirable low frequency sounds (standing wave
Standing wave
In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...
s, etc.) by building a resonator tuned to the problem frequency, thereby eliminating it.
Helmholtz resonators are also used to build acoustic liners for reducing the noise of aircraft engines, for example. These acoustic liners are made of two components:
- a simple sheet of metal (or other material) perforated with little holes spaced out in a regular or irregular pattern; this is called a 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 of 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" (DOF meaning Degrees Of Freedom), as opposed to "single DOF liners".
This effect might also be used to reduce skin friction drag on aircraft wings by 40%.
Sources
- Oxford Physics Teaching, History Archive, "Exhibit 3 - Helmholtz resonators" (archival photograph)
- HyperPhysics Acoustic Laboratory
- HyperPhysics Cavity Resonance
- Beverage Bottles as Helmholtz ResonatorsScience Project Idea for Students
- Helmholtz Resonance (web site on music acoustics)