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Phase Velocity in Axial Direction Formula

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Phase Velocity in Axial Direction refers to the speed at which the phase of a wave propagates along the axis of a structure or medium. Check FAQs

v pe = \frac{p}{\sqrt{μ r \cdot ε \cdot ((p^{2}) + {(π \cdot d)}^{2})}}

v_pe - Phase Velocity in Axial Direction?p - Helix Pitch?μ_r - Relative Permeability?ε - Permittivity of Dielectric?d - Diameter of Helix?π - Archimedes' constant?

Phase Velocity in Axial Direction Example

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Here is how the Phase Velocity in Axial Direction equation looks like with Values.

Here is how the Phase Velocity in Axial Direction equation looks like with Units.

Here is how the Phase Velocity in Axial Direction equation looks like.

0.125 = \frac{4.5}{\sqrt{1.3 \cdot 7.8 \cdot (({4.5}^{2}) + {(3.1416 \cdot 3.3)}^{2})}}

0.125m/s = \frac{4.5m}{\sqrt{1.3H/m \cdot 7.8F/m \cdot (({4.5m}^{2}) + {(3.1416 \cdot 3.3m)}^{2})}}

0.125 = \frac{4.5}{\sqrt{1.3 \cdot 7.8 \cdot (({4.5}^{2}) + {(3.1416 \cdot 3.3)}^{2})}}

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Phase Velocity in Axial Direction Solution

Follow our step by step solution on how to calculate Phase Velocity in Axial Direction?

FIRST Step Consider the formula

v pe = \frac{p}{\sqrt{μ r \cdot ε \cdot ((p^{2}) + {(π \cdot d)}^{2})}}

Next Step Substitute values of Variables

∴

v pe = \frac{4.5m}{\sqrt{1.3H/m \cdot 7.8F/m \cdot (({4.5m}^{2}) + {(π \cdot 3.3m)}^{2})}}

Next Step Substitute values of Constants

∴

v pe = \frac{4.5m}{\sqrt{1.3H/m \cdot 7.8F/m \cdot (({4.5m}^{2}) + {(3.1416 \cdot 3.3m)}^{2})}}

Next Step Prepare to Evaluate

∴

v pe = \frac{4.5}{\sqrt{1.3 \cdot 7.8 \cdot (({4.5}^{2}) + {(3.1416 \cdot 3.3)}^{2})}}

Next Step Evaluate

∴

v pe = 0.125039461283172m/s

LAST Step Rounding Answer

∴

v pe = 0.125m/s

Phase Velocity in Axial Direction Formula Elements

Variables

Constants

Functions

Phase Velocity in Axial Direction

Phase Velocity in Axial Direction refers to the speed at which the phase of a wave propagates along the axis of a structure or medium.

Symbol: v_pe

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Phase Velocity in Axial Direction

Helix Pitch

Helix Pitch, which represents the distance between consecutive turns along the helix.

Symbol: p

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Helix Pitch

Relative Permeability

Relative Permeability is the ratio of effective permeability of a particular fluid at a particular saturation to absolute permeability of that fluid at total saturation.

Symbol: μ_r

Measurement: Magnetic PermeabilityUnit: H/m

Note: Value can be positive or negative.

Formulas to find Relative Permeability

Permittivity of Dielectric

Permittivity of Dielectric refers to the ability to store electrical energy in an electric field.

Symbol: ε

Measurement: PermittivityUnit: F/m

Note: Value can be positive or negative.

Formulas to find Permittivity of Dielectric

Diameter of Helix

Diameter of Helix is the distance across the widest part of the helix.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Diameter of Helix

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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How to Evaluate Phase Velocity in Axial Direction?

Phase Velocity in Axial Direction evaluator uses Phase Velocity in Axial Direction = Helix Pitch/(sqrt(Relative Permeability*Permittivity of Dielectric*((Helix Pitch^2)+(pi*Diameter of Helix)^2))) to evaluate the Phase Velocity in Axial Direction, The Phase Velocity in Axial Direction formula is defined refers to the speed at which the phase of a wave propagates along the axis of a structure or medium. It describes how quickly the phase of the wave changes as it travels along the length of the structure or medium in the axial (longitudinal) direction. Phase Velocity in Axial Direction is denoted by v_pe symbol.

How to evaluate Phase Velocity in Axial Direction using this online evaluator? To use this online evaluator for Phase Velocity in Axial Direction, enter Helix Pitch (p), Relative Permeability (μ_r), Permittivity of Dielectric (ε) & Diameter of Helix (d) and hit the calculate button.

FAQs on Phase Velocity in Axial Direction

What is the formula to find Phase Velocity in Axial Direction?

The formula of Phase Velocity in Axial Direction is expressed as Phase Velocity in Axial Direction = Helix Pitch/(sqrt(Relative Permeability*Permittivity of Dielectric*((Helix Pitch^2)+(pi*Diameter of Helix)^2))). Here is an example- 0.125039 = 4.5/(sqrt(1.3*7.8*((4.5^2)+(pi*3.3)^2))).

How to calculate Phase Velocity in Axial Direction?

With Helix Pitch (p), Relative Permeability (μ_r), Permittivity of Dielectric (ε) & Diameter of Helix (d) we can find Phase Velocity in Axial Direction using the formula - Phase Velocity in Axial Direction = Helix Pitch/(sqrt(Relative Permeability*Permittivity of Dielectric*((Helix Pitch^2)+(pi*Diameter of Helix)^2))). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Phase Velocity in Axial Direction be negative?

Yes, the Phase Velocity in Axial Direction, measured in Speed can be negative.

Which unit is used to measure Phase Velocity in Axial Direction?

Phase Velocity in Axial Direction is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Phase Velocity in Axial Direction can be measured.

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Phase Velocity in Axial Direction Formula

Phase Velocity in Axial Direction Example

Phase Velocity in Axial Direction Solution

Phase Velocity in Axial Direction Formula Elements

Other formulas in Beam Tube category

How to Evaluate Phase Velocity in Axial Direction?

FAQs on Phase Velocity in Axial Direction

Variable Name