Dielectric Resonators, Resonant Frequency, and Dielectric Constant?

[HMS-776]

Hello,

I have been trying to better understand the effects of dielectrics in resonant cavities.

I read that the addition of a dielectric in a resonant cavity will reduce the resonant frequency of the cavity.

My questions:

Is there any relation to the reduction of the resonant frequency and the dielectric constant of the dielectric placed in a resonant cavity?

Would it be possible to build a small resoant cavity (less than 1 foot in volume) which had a resonant frequency in the audio range by adding a dielectric to it?

 

[marcusl]

Yes, a dielectric will reduce the resonant frequency of a cavity. If the dielectric fills the cavity, then the frequency is reduced by approximately the square root of the dielectric constant.

No, you can't build a small cavity that resonates at audio because at least one dimension of the cavity must be wavelength/2. The wavelength of a 1 kHz wave is 3x10^5 m or 3,000 km--about the width of the United States. Filling it with water, which has about the highest dielectric constant (81) of any ordinary material, drops the physical dimensions by 9, to about 2,000 km. Still big compared to one foot...

 

[hamza_1980]

i need problems and solutions about dielectric material

 

[marcusl]

Please start a new thread on your topic, and provide more information--your request is very vague.

 

[alphysicist]

Thank you for your questions!

Yes, there is a direct relation between the reduction of resonant frequency and the dielectric constant of the material placed in a resonant cavity. The dielectric constant, also known as relative permittivity, is a measure of how much a material can store electric charge. When a dielectric material is placed in a resonant cavity, it affects the electric field distribution and thus alters the resonant frequency of the cavity. The higher the dielectric constant, the lower the resonant frequency will be.

It is certainly possible to build a small resonant cavity with a resonant frequency in the audio range by adding a dielectric material. In fact, dielectric resonators are commonly used in microwave and RF circuits to achieve specific resonant frequencies. However, in order to achieve an audio frequency resonant cavity, the dielectric material would need to have a very high dielectric constant and the cavity would need to be carefully designed to achieve the desired frequency.