A brass, spherical Helmholtz resonator based on his original design, circa 1890–1900.
Helmholtz resonance, also known as wind throb, refers to the phenomenon of air resonance in a cavity, an effect named after the German physicist Hermann von Helmholtz.[1] This type of resonance occurs when air is forced in and out of a cavity, causing the air inside to vibrate at a specific natural frequency. The principle is widely observable in everyday life, notably when blowing across the top of a bottle, resulting in a resonant tone.
The concept of Helmholtz resonance is fundamental in various fields, including acoustics, engineering, and physics. The resonator itself, termed a Helmholtz resonator, consists of two key components: a cavity and a neck. The size and shape of these components are crucial in determining the resonant frequency, which is the frequency at which the system naturally oscillates.
In the context of acoustics, Helmholtz resonance is instrumental in the design and analysis of musical instruments, architectural acoustics, and sound engineering. It is also utilized in automotive engineering for noise reduction and in designing exhaust systems.
The underlying principle involves the vibration of the air mass in the neck of the resonator, acting analogously to a mass on a spring. When external forces, such as airflow, disturb this air mass, it oscillates and causes the air within the cavity to resonate. This phenomenon is characterized by its sharp and high-amplitude resonance curve, making it distinct from other types of acoustic resonance.
Since its conceptualization in the 19th century, Helmholtz resonance has continued to be a subject of study and application, illustrating the interplay between simple physical systems and complex vibrational phenomena.
Helmholtz described in his 1862 book On the Sensations of Tone an apparatus able to pick out specific frequencies from a complex sound. The Helmholtz resonator, as it is now called, consists of a rigid container of a known volume, nearly spherical in shape, with a small neck and hole in one end and a larger hole in the other end to emit the sound.
When the resonator's 'nipple' is placed inside one's ear, a specific frequency of the complex sound can be picked out and heard clearly. In his book Helmholtz explains: When we "apply a resonator to the ear, most of the tones produced in the surrounding air will be considerably damped; but if the proper tone of the resonator is sounded, it brays into the ear most powerfully…. The proper tone of the resonator may even be sometimes heard cropping up in the whistling of the wind, the rattling of carriage wheels, the splashing of water."
A set of varied size resonators was sold to be used as discrete acoustic filters for the spectral analysis of complex sounds. There is also an adjustable type, called a universal resonator, which consists of two cylinders, one inside the other, which can slide in or out to change the volume of the cavity over a continuous range. An array of 14 of this type of resonator has been employed in a mechanical Fourier sound analyzer. This resonator can also emit a variable-frequency tone when driven by a stream of air in the "tone variator" invented by William Stern, 1897.[2]
When air is forced into a cavity, the pressure inside increases. When the external force pushing the air into the cavity is removed, the higher-pressure air inside will flow out. Due to the inertia of the moving air 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 oscillations increasing and decreasing asymptotically after the sound starts and stops.
The port (the neck of the chamber) is placed in the ear, allowing the experimenter to hear the sound and to determine its loudness. The resonant mass of air in the chamber is set in motion through the second hole, which is larger and doesn't have a neck.
A gastropod seashell can form a Helmholtz resonator with low Q factor, amplifying many frequencies, resulting in the "sounds of the sea".
The term Helmholtz resonator is now more generally applied to include bottles from which sound is generated by blowing air across the mouth of the bottle. In this case the length and diameter of the bottle neck also contribute to the resonance frequency and its Q factor.
By one definition a Helmholtz resonator augments the amplitude of the vibratory motion of the enclosed air in a chamber by taking energy from sound waves passing in the surrounding air. In the other definition the sound waves are generated by a uniform stream of air flowing across the open top of an enclosed volume of air.
is the equivalent length of the neck with end correction, which can be calculated as:, where is the actual length of the neck and is the hydraulic diameter of the neck;[4]
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.[5] 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 formulae can still be derived analytically, with similar physical explanations (although some differences matter).[6] Furthermore, if the mean flow over the resonator is high (typically with a Mach number above 0.3), some corrections must be applied.
Applications
Automotive
Helmholtz resonance sometimes occurs when a slightly open single car window makes a very loud sound, also called side window buffeting or wind throb.[7] Because cars have a large volume, the frequency of the wind throb is quite low.[8]
Helmholtz resonance finds application in internal combustion engines (see Airbox), subwoofers and acoustics. Intake systems described as 'Helmholtz Systems' have been used in the Chrysler V10 engine built for both the Dodge Viper and the Ram pickup truck, and several of the Buell tube-frame series of motorcycles.
The theory of Helmholtz resonators is 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 are also used to reduce potentially loud 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 two-stroke engines, a Helmholtz resonator is used to remove the need for a reed valve. A similar effect is also used in the exhaust system of most two-stroke engines, using a reflected pressure pulse to supercharge the cylinder (see Kadenacy effect).
During the early 2010s, some Formula 1 teams used Helmholtz resonators in their cars' exhaust systems to help even out the flow of gasses that were being used to seal the edges of their diffusers as part of their exhaust blow diffuser systems. [9]
Aircraft
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 20%.[10]
Vitruvius, a 1st-century B.C. Roman architect, described the use of bronze or pottery resonators in classical theater design.[11][12]
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, and putting absorbing material inside, thereby reducing it.[citation needed]
Music (instruments and amplification)
In all stringed instruments, from the veena or sitar to the modern guitar and violin, the response curve of the instrument consists of a series of Helmholtz resonance modes associated with the size and shape of the resonance cavity (harmonics of the fundamental cavity mode), as well as vibration damping from absorption by the resonance cavity material (typically wood). An ocarina[13] is essentially a Helmholtz resonator where the combined area of the opened finger holes determines the note played by the instrument.[14] The West African djembe is related to a Helmholtz resonator with a small neck area, giving it a deep bass tone, but its stretched skin, strongly coupled to the cavity makes it a more complex, and musically interesting, resonant system. It has been in use for thousands of years.[citation needed] Conversely, the human mouth is effectively a Helmholtz resonator when it is used in conjunction with a jaw harp,[15]shepherd's whistle,[citation needed]nose whistle, nose flute. The nose blows air through an open nosepiece, into an air duct, and across an edge adjacent to the open mouth, creating the resonator. The volume and shape of the mouth cavity augments the pitch of the tone.[16]
Helmholtz resonance is also used in bass-reflex speaker enclosures, with the compliance of the air mass inside the enclosure and the mass of air in the port forming a Helmholtz resonator. By tuning the resonant frequency of the Helmholtz resonator to the lower end of the loudspeaker's usable frequency range, the speaker's low-frequency performance is improved.
Other
Helmholtz resonance is one of the principles behind the way piezoelectric buzzers work: a piezoelectric disc acts as the excitation source, but it relies on the acoustic cavity resonance to produce an audible sound.[17]
↑ "End correction at flue pipe mouth". Johan Liljencrants on organs, pipes, air supply. September 30, 2006. Archived from the original on February 19, 2020. Retrieved October 29, 2018.
↑ Greene, Chad A.; Argo IV, Theodore F.; Wilson, Preston S. (2009). A Helmholtz resonator experiment for the Listen Up project. Proceedings of Meetings on Acoustics. ASA. p.025001. doi:10.1121/1.3112687.
↑ For a survey of prehistoric ocarina-type instruments and a linguistic analysis of the possible origins of the word ocarina, cf. Perono Cacciafoco, Francesco. (2019). A Prehistoric 'Little Goose': A New Etymology for the Word 'Ocarina'. Annals of the University of Craiova: Series Philology, Linguistics, XLI, 1-2: 356-369, Paper.
Perono Cacciafoco, Francesco. (2019). A Prehistoric 'Little Goose': A New Etymology for the Word 'Ocarina'. Annals of the University of Craiova: Series Philology, Linguistics, XLI, 1-2: 356-369, Paper
In physics, resonance refers to a wide class of phenomena that arise as a result of matching temporal or spatial periods of oscillatory objects. For an oscillatory dynamical systems driven by a time-varying external force, resonance occurs when the frequency of the external force coincides with the natural frequency of the system. Resonance can occur in various systems, such as mechanical, electrical, or acoustic systems, and it is desirable in certain applications, such as musical instruments or radio receivers. Resonance can also be undesirable, leading to excessive vibrations or even structural failure in some cases.
In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect to time, and the oscillations at different points throughout the wave are in phase. The locations at which the absolute value of the amplitude is minimum are called nodes, and the locations where the absolute value of the amplitude is maximum are called antinodes.
The ocarina is a wind musical instrument; it is a type of vessel flute. Variations exist, but a typical ocarina is an enclosed space with four to twelve finger holes and a mouthpiece that projects from the body. It is traditionally made from clay or ceramic, but other materials are also used, such as plastic, wood, glass, metal, or bone.
In physics and engineering, the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy lost in one radian of the cycle of oscillation. Q factor is alternatively defined as the ratio of a resonator's centre frequency to its bandwidth when subject to an oscillating driving force. These two definitions give numerically similar, but not identical, results. Higher Q indicates a lower rate of energy loss and the oscillations die out more slowly. A pendulum suspended from a high-quality bearing, oscillating in air, has a high Q, while a pendulum immersed in oil has a low one. Resonators with high quality factors have low damping, so that they ring or vibrate longer.
A sound box or sounding box is an open chamber in the body of a musical instrument which modifies the sound of the instrument, and helps transfer that sound to the surrounding air. Objects respond more strongly to vibrations at certain frequencies, known as resonances. The frequency and strength of the resonances of the body of a musical instrument have a significant impact on the tone quality it produces. The air inside the chamber has its own resonances, and these interact with the resonances of the body, altering the resonances of the instrument as a whole. The sound box typically adds resonances at lower frequencies, enhancing the lower-frequency response of the instrument.
Room acoustics is a subfield of acoustics dealing with the behaviour of sound in enclosed or partially-enclosed spaces. The architectural details of a room influences the behaviour of sound waves within it, with the effects varying by frequency. Acoustic reflection, diffraction, and diffusion can combine to create audible phenomena such as room modes and standing waves at specific frequencies and locations, echos, and unique reverberation patterns.
A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator can be either electromagnetic or mechanical. Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones. Another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of very precise frequency.
A quartz crystal microbalance (QCM) measures a mass variation per unit area by measuring the change in frequency of a quartz crystal resonator. The resonance is disturbed by the addition or removal of a small mass due to oxide growth/decay or film deposition at the surface of the acoustic resonator. The QCM can be used under vacuum, in gas phase and more recently in liquid environments. It is useful for monitoring the rate of deposition in thin-film deposition systems under vacuum. In liquid, it is highly effective at determining the affinity of molecules to surfaces functionalized with recognition sites. Larger entities such as viruses or polymers are investigated as well. QCM has also been used to investigate interactions between biomolecules. Frequency measurements are easily made to high precision ; hence, it is easy to measure mass densities down to a level of below 1 μg/cm2. In addition to measuring the frequency, the dissipation factor is often measured to help analysis. The dissipation factor is the inverse quality factor of the resonance, Q−1 = w/fr ; it quantifies the damping in the system and is related to the sample's viscoelastic properties.
Acoustic resonance is a phenomenon in which an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration.
Acoustic waves are a type of energy propagation through a medium by means of adiabatic loading and unloading. Important quantities for describing acoustic waves are acoustic pressure, particle velocity, particle displacement and acoustic intensity. Acoustic waves travel with a characteristic acoustic velocity that depends on the medium they're passing through. Some examples of acoustic waves are audible sound from a speaker, seismic waves, or ultrasound used for medical imaging.
An acoustic guitar is a musical instrument in the string family. When a string is plucked, its vibration is transmitted from the bridge, resonating throughout the top of the guitar. It is also transmitted to the side and back of the instrument, resonating through the air in the body, and producing sound from the sound hole. While the original, general term for this stringed instrument is guitar, the retronym 'acoustic guitar' – often used to indicate the steel stringed model – distinguishes it from an electric guitar, which relies on electronic amplification. Typically, a guitar's body is a sound box, of which the top side serves as a sound board that enhances the vibration sounds of the strings. In standard tuning the guitar's six strings are tuned (low to high) E2 A2 D3 G3 B3 E4.
Violin acoustics is an area of study within musical acoustics concerned with how the sound of a violin is created as the result of interactions between its many parts. These acoustic qualities are similar to those of other members of the violin family, such as the viola.
Bass traps are acoustic energy absorbers which are designed to damp low-frequency sound energy with the goal of attaining a flatter low-frequency (LF) room response by reducing LF resonances in rooms. They are commonly used in recording studios, mastering rooms, home theatres and other rooms built to provide a critical listening environment. Like all acoustically absorptive devices, they function by turning sound energy into heat through friction.
A nose whistle is a wind instrument played with the nose and mouth cavity. Often made of wood, they are also constructed with plastic, clay, or sheet metal.
Vocal resonance may be defined as "the process by which the basic product of phonation is enhanced in timbre and/or intensity by the air-filled cavities through which it passes on its way to the outside air." Throughout the vocal literature, various terms related to resonation are used, including: amplification, filtering, enrichment, enlargement, improvement, intensification, and prolongation. Acoustic authorities would question many of these terms from a strictly scientific perspective. However, the main point to be drawn from these terms by a singer or speaker is that the result of resonation is to make a better sound, or at least suitable to a certain esthetical and practical domain.
A microwave cavity or radio frequency cavity is a special type of resonator, consisting of a closed metal structure that confines electromagnetic fields in the microwave or RF region of the spectrum. The structure is either hollow or filled with dielectric material. The microwaves bounce back and forth between the walls of the cavity. At the cavity's resonant frequencies they reinforce to form standing waves in the cavity. Therefore, the cavity functions similarly to an organ pipe or sound box in a musical instrument, oscillating preferentially at a series of frequencies, its resonant frequencies. Thus it can act as a bandpass filter, allowing microwaves of a particular frequency to pass while blocking microwaves at nearby frequencies.
An acoustic metamaterial, sonic crystal, or phononic crystal is a material designed to control, direct, and manipulate sound waves or phonons in gases, liquids, and solids. Sound wave control is accomplished through manipulating parameters such as the bulk modulus β, density ρ, and chirality. They can be engineered to either transmit, or trap and amplify sound waves at certain frequencies. In the latter case, the material is an acoustic resonator.
A vessel flute is a type of flute with a body which acts as a Helmholtz resonator. The body is vessel-shaped, not tube- or cone-shaped; that is, the far end is closed.
A whistle is a device that makes sound from air blown from one end forced through a small opening at the opposite end. They are shaped in a way that allows air to oscillate inside of a chamber in an unstable way. The physical theory of the sound-making process is an example of the application of fluid dynamics or hydrodynamics and aerodynamics. The principles relevant to whistle operation also have applications in other areas, such as fluid flow measurement.
A loop-gap resonator (LGR) is an electromagnetic resonator that operates in the radio and microwave frequency ranges. The simplest LGRs are made from a conducting tube with a narrow slit cut along its length. The LGR dimensions are typically much smaller than the free-space wavelength of the electromagnetic fields at the resonant frequency. Therefore, relatively compact LGRs can be designed to operate at frequencies that are too low to be accessed using, for example, cavity resonators. These structures can have very sharp resonances making them useful for electron spin resonance (ESR) experiments, and precision measurements of electromagnetic material properties.
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