Cavity resonator
Cavity resonators are structures in which can form a standing wave, usually with different modes by resonance.
In the high-frequency technology cavity resonators are used at frequencies above about 1 GHz instead of resonant circuits, because they have lower losses and thus a high quality factor. In particle accelerators, they serve - often referred to herein as cavities - to accelerate electrically charged particles.
On acoustic cavity resonators, for example, based many musical instruments.
- 2.1 Examples of both sides open resonators
- 2.2 Examples of Blind tubes
- 2.3 Examples of closed resonators
Cavity resonators in the high-frequency technology
With the aid of cavity resonators can also develop good filter for very high frequencies.
The calculation of all the natural frequencies of a cuboid space can be performed with the 1896, described by Lord Rayleigh formula:
This is the medium-dependent rate constant, and the dimensions of space, so the length, width and height, and and denote the orders of the modes in the respective directions. One of the positive integer parameter or can be set to zero.
Example calculation of the resonance frequencies of electromagnetic waves in a cavity resonator
A cavity resonator has an infinite number of resonant frequencies, since the atomic numbers do not end up like in the example table for three. The lowest resonant frequencies can still be readily separated. Higher resonance frequencies are, however, always closer to each other and even merge. Thereby, a separation due to the finite bandwidth is not possible.
In order to produce a resonance in the cavity, energy must be supplied. As cavity resonators have a damping such resonance sounds from again when no power is supplied. The power is supplied typically by a shape of the waveguide. The coupling of the waveguide depends on the nature of the waveguide and the modes that are to be encouraged and can be divided into capacitive and inductive coupling.
Application of high-frequency cavity resonators
- In the microwave technique: One- and coupling- resonators in klystrons, shaft diameter
- A magnetron contains many coupled cavity resonators of the same frequency
- Pillbox ( cavity)
- Particle acceleration, see linear accelerator
Cavity resonators in acoustics
In acoustics on both sides and open on one side and closed cavity resonators play a major role.
Both sides open tubes have their fundamental resonance at half the wavelength of sound.
Examples of both sides open resonators
- Flute: By blowing technique and handles the fundamental and even harmonics ( one or more octaves higher) can be excited. The effective tube length is determined by the with the fingers behind the other closed holes.
- Resonance tubes under the sounds of xylophones and metallophonic
- Kundt's tube.
Examples of Blind tubes
- , Stopped organ pipes and cylindrical reed instruments ( clarinet). Here are odd harmonics and even harmonics excited. The fundamental resonance corresponds to a quarter of the acoustic wavelength.
Examples of closed resonators
- Enclosed spaces. Small spaces have very discrete eigenfrequencies. These natural frequencies are now referred to throughout as spatial modes. Superimposing itself on large spaces such as churches all room modes to a continuum - occurs Hall.
- Helmholtz resonator and bass reflex speakers have basic resonances, based on other laws. Here, the air mass oscillates in the neck or in the bass reflex tube against the elasticity of the volume, the fundamental resonances are lower than one might expect, the geometric dimensions.
- Reinforcement effect in photoacoustic spectroscopy. The sound intensity at low concentrations is low and by acoustic resonance, the sound intensity to be raised in the cavity by a factor of 100.