Name: electromagnetic modes in a microwave cavity
Uploaded: 2023-09-18T17:11:21.000Z
Duration: 1 min 28 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Physical Science

PS.7

PS.7.a

Standing Waves in a Cavity

Mikrowellenherde verwenden elektromagnetische Wellen, um Lebensmittel zu erhitzen.
Die meisten Lebensmittel enthalten polare Moleküle wie Wasser, die mit dem elektrischen Wechselfeld hin und her wechseln. Beim Wenden reiben sich die Moleküle mit anderen Molekülen, wodurch Wärme erzeugt wird.
Die Mikrowellenkammer fungiert als Resonanzresonator, in dem stehende elektromagnetische Wellen durch Reflexion von der Metalloberfläche gebildet werden. Die beiden metallischen Flächen werden in Knotenebenen angeordnet.
Der Abstand zwischen den Ebenen muss also ein ganzzahliges Vielfaches der halben Wellenlänge sein.
Die Wellenlängen, die diese Bedingung erfüllen, werden als charakteristische Wellenlängen bezeichnet, und die entsprechenden Frequenzen werden als charakteristische Frequenzen bezeichnet.
Jede charakteristische Frequenz, Wellenform und jedes Knotenmuster stellt eine Reihe von Normalmoden dar.
Eine typische Mikrowelle für den Haushalt läuft beispielsweise mit 2,4 Gigahertz, was einer Wellenlänge entspricht, die von den Wassermolekülen leicht absorbiert wird.
Diese Wellenlänge hat Knoten im Abstand von 6,1 Zentimetern, was bedeutet, dass das Essen an diesen Stellen kalt und an den Antinodien maximal erhitzt wird.
Der Drehteller der Mikrowelle wird also gedreht, um eine gleichmäßige Wärmeverteilung zu erreichen.

<ol>
	<li>Young, H.D. und Freedman, R.A. (2012). Universitätsphysik mit moderner Physik. San Francisco, Kalifornien: Pearson. Abschnitt 32.5; Seite 1071.</li>
</ol>

stehende wellen in einer kavität

Eine Haushaltsmikrowelle und Laser sind Beispiele für stehende elektromagnetische Wellen in einer Kavität. Wenn zwei leitende Metallplatten parallel an den Knotenebenen platziert werden, entsteht eine Kavität, in der stehende Wellen gebildet werden. Die Kavität zwischen den beiden Ebenen ist analog zu einer gespannten Saite, die an den Punkten x = 0 und x = L gehalten wird. Dabei muss der Abstand 'L' zwischen den beiden Ebenen ein ganzzahliges Vielfaches von der Hälfte der Wellenlänge sein. Die Wellenlängen, die diese Bedingung erfüllen, werden durch folgende Formel gegeben: Die entsprechenden Frequenzen sind:

<img alt="Equation1" src="/files/ftp_upload/14213/14213_Equation_1.png" style="text-align: center; height: 40px;" />

Jede charakteristische Frequenz, Wellenform und Knotenmuster bildet eine Reihe von Normalmoden. Die Wellenlänge kann durch Messung der Knotenpositionen abgeschätzt werden. Wenn die Frequenz bekannt ist, kann auch die Wellengeschwindigkeit bestimmt werden.

<img alt="Equation2" src="/files/ftp_upload/14213/14213_Equation_2.png" style="text-align: center; height: 40px;" />

Neben leitenden Oberflächen kann die Reflexion elektromagnetischer Wellen auch an einer Grenzfläche zwischen zwei isolierenden Materialien mit unterschiedlicher dielektrischer oder magnetischer Eigenschaft auftreten. Das mechanische Analogon ist eine Kreuzung zweier Saiten mit gleicher Spannung, aber unterschiedlicher linearer Massendichte. Typischerweise wird eine Welle, die auf eine solche Begrenzungsfläche trifft, teilweise in das zweite Material übertragen und teilweise in das erste zurück reflektiert. Zum Beispiel wird Licht durch ein Glasfenster übertragen, aber seine Oberflächen reflektieren auch das Licht.

Stehende Wellen in einer Kavität

Eine Mikrowelle und Laser für den Haushalt sind Beispiele für stehende elektromagnetische Wellen in einem Hohlraum. Werden zwei leitende Metallplatten parallel an der ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

Electromagnetic Waves

Elektromagnetische Wellen

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

electromagnetic modes in a microwave cavity

Electromagnetic waves can form standing patterns inside a cavity. Household microwaves and lasers are common examples of this effect. When two conducting metal plates are placed parallel at the nodal planes, they create a space where standing waves can exist.

The cavity between the plates works like a stretched string fixed at x = 0 and x = L. The distance L must be an integer multiple of half a wavelength. The wavelengths that meet this condition have matching frequencies, and each frequency, wave shape, and node pattern is a normal mode.

Node positions can be measured to estimate the wavelength. If the frequency is known, the wave speed can also be found. Electromagnetic waves can also reflect at the boundary between two insulating materials with different dielectric or magnetic properties.

This kind of boundary acts like a junction between two strings with the same tension but different linear mass density. A wave that reaches the boundary is partly transmitted into the second material and partly reflected back. Light passing through a glass window is one example, since the surfaces transmit some light and also reflect some of it.

Electromagnetic Modes in a Microwave Cavity

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Electromagnetic waves can form standing patterns inside a cavity. Household microwaves and lasers are common examples of this effect. When two conducting metal plates are placed parallel at the nodal planes, they create a space where standing waves can exist. The cavity between the plates works like a stretched string fixed at x = 0 and x = L. The distance L must be an integer multiple of half a wavelength. The wavelengths that meet this condition have matching frequencies, and each frequency,...

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Learn how standing electromagnetic waves form in a cavity, why only certain wavelengths fit, and how reflections create partial transmission at boundaries.

Electromagnetic Modes in a Microwave Cavity | JoVE K12

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PS.7.b

Electromagnetic Modes in a Microwave Cavity

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