## Radian Cutoff Angular Frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance)
ωcm = (m*pi*[c])/(nr*pd)
This formula uses 2 Constants, 4 Variables
Constants Used
[c] - Light speed in vacuum Value Taken As 299792458.0 Meter/Second
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Cutoff Angular Frequency - (Measured in Radian per Second) - Cutoff Angular Frequency representing the maximum frequency for which a particular mode of a waveguide or transmission line can be supported.
Mode Number - Mode Number the mode number indicates the number of half-wavelengths that fit into the given space.
Refractive Index - Refractive index is a dimensionless quantity that describes how much light is slowed down or refracted when entering a medium compared to its speed in a vacuum.
Plate Distance - (Measured in Meter) - Plate Distance typically refers to the separation between the conductive elements.
STEP 1: Convert Input(s) to Base Unit
Mode Number: 4 --> No Conversion Required
Refractive Index: 2 --> No Conversion Required
Plate Distance: 21.23 Centimeter --> 0.2123 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ωcm = (m*pi*[c])/(nr*pd) --> (4*pi*[c])/(2*0.2123)
Evaluating ... ...
ωcm = 8872593345.77887
STEP 3: Convert Result to Output's Unit
8872593345.77887 Radian per Second --> No Conversion Required
8872593345.77887 8.9E+9 Radian per Second <-- Cutoff Angular Frequency
(Calculation completed in 00.019 seconds)
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## Credits

Created by Gowthaman N
Vellore Institute of Technology (VIT University), Chennai
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Chandigarh University (CU), Punjab
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## < 12 Guided Waves in Field Theory Calculators

Characteristic Impedance of Line
Characteristic Impedance = sqrt(Magnetic Permeability*pi*10^-7/Dielectric Permitivitty)*(Plate Distance/Plate Width)
Total Resistance of Coaxial Cable
Total Resistance of Coaxial Cable = 1/(2*pi*Skin Depth*Electrical Conductivity)*(1/Inner Radius of Coaxial Cable+1/Outer Radius of Coaxial Cable)
Inductance per unit Length of Coaxial Cable
Inductance per unit length of Coaxial Cable = Magnetic Permeability/2*pi*ln(Outer Radius of Coaxial Cable/Inner Radius of Coaxial Cable)
Conductance of Coaxial Cable
Conductance of Coaxial Cable = (2*pi*Electrical Conductivity)/ln(Outer Radius of Coaxial Cable/Inner Radius of Coaxial Cable)
Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance)
Inner Resistance of Coaxial Cable
Inner Resistance of Coaxial Cable = 1/(2*pi*Inner Radius of Coaxial Cable*Skin Depth*Electrical Conductivity)
Outer Resistance of Coaxial Cable
Outer Resistance of Coaxial Cable = 1/(2*pi*Skin Depth*Outer Radius of Coaxial Cable*Electrical Conductivity)
Inductance between Conductors
Conductor Inductance = Magnetic Permeability*pi*10^-7*Plate Distance/(Plate Width)
Magnitude of Wavevector
Wave Vector = Angular Frequency*sqrt(Magnetic Permeability*Dielectric Permitivitty)
Skin Effect Resistivity
Skin Effect Resistivity = 2/(Electrical Conductivity*Skin Depth*Plate Width)
Cutoff Wavelength
Cutoff Wavelength = (2*Refractive Index*Plate Distance)/Mode Number
Phase Velocity in Microstrip Line
Phase Velocity = [c]/sqrt(Dielectric Permitivitty)

## Radian Cutoff Angular Frequency Formula

Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance)
ωcm = (m*pi*[c])/(nr*pd)

## How does the mode number affect the angular frequency of a wave in a waveguide?

As the mode number increases, the angular frequency of a wave in a waveguide also increases. This is because higher mode numbers correspond to shorter wavelengths, which in turn require higher frequencies for propagation within the waveguide's confined dimensions.

## How to Calculate Radian Cutoff Angular Frequency?

Radian Cutoff Angular Frequency calculator uses Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance) to calculate the Cutoff Angular Frequency, The Radian Cutoff Angular Frequency formula is a fundamental relationship in waveguiding and transmission line theory. It allows us to calculate the angular frequency of a wave propagating within a waveguide or transmission line, given its mode number, the speed of light, the refractive index of the medium, and the waveguide's characteristic dimension. Cutoff Angular Frequency is denoted by ωcm symbol.

How to calculate Radian Cutoff Angular Frequency using this online calculator? To use this online calculator for Radian Cutoff Angular Frequency, enter Mode Number (m), Refractive Index (nr) & Plate Distance (pd) and hit the calculate button. Here is how the Radian Cutoff Angular Frequency calculation can be explained with given input values -> 8.9E+9 = (4*pi*[c])/(2*0.2123).

### FAQ

What is Radian Cutoff Angular Frequency?
The Radian Cutoff Angular Frequency formula is a fundamental relationship in waveguiding and transmission line theory. It allows us to calculate the angular frequency of a wave propagating within a waveguide or transmission line, given its mode number, the speed of light, the refractive index of the medium, and the waveguide's characteristic dimension and is represented as ωcm = (m*pi*[c])/(nr*pd) or Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance). Mode Number the mode number indicates the number of half-wavelengths that fit into the given space, Refractive index is a dimensionless quantity that describes how much light is slowed down or refracted when entering a medium compared to its speed in a vacuum & Plate Distance typically refers to the separation between the conductive elements.
How to calculate Radian Cutoff Angular Frequency?
The Radian Cutoff Angular Frequency formula is a fundamental relationship in waveguiding and transmission line theory. It allows us to calculate the angular frequency of a wave propagating within a waveguide or transmission line, given its mode number, the speed of light, the refractive index of the medium, and the waveguide's characteristic dimension is calculated using Cutoff Angular Frequency = (Mode Number*pi*[c])/(Refractive Index*Plate Distance). To calculate Radian Cutoff Angular Frequency, you need Mode Number (m), Refractive Index (nr) & Plate Distance (pd). With our tool, you need to enter the respective value for Mode Number, Refractive Index & Plate Distance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well. Let Others Know