Cylindrical cavity resonator problem

[Dhruv]

Homework Statement

Q. A cylindrical cavity resonator has diameter of 24 mm and length 20 mm. The dominant mode and the lowest frequency band are operated as ? I am providing a picture of problem to show the options given to me.

I solved the problem by calculating resonant frequency for cavity resonator and my answer is coming to be (a).

But on considering the condition " TM₁₁₀ mode is dominant where 2a > d , and that the TE₁₁₁ mode is dominant when d > 2a. My answer is coming to be (d).
Then which one should I consider of two options.

Homework Equations

The Attempt at a Solution

I am providing pictures of my work below.

 

[KataKoniK]

it is important to carefully consider all the factors and conditions before making a decision. In this case, the condition given states that for the TM110 mode to be dominant, the diameter (d) of the cavity must be greater than twice the radius (a).

Based on the given dimensions of the cavity (d = 24 mm, a = 12 mm), it is clear that the condition for the TM110 mode to be dominant is not met. Therefore, the TE111 mode would be the dominant mode in this case.

Hence, the correct answer would be (d) - TE111 mode. It is important to carefully analyze the given information and conditions before solving the problem to ensure accurate results.