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Guo Formula of Linear Dispersion Relation for Wave Number Formula

GoWave Number of Convenient Empirical Explicit Approximation Formula

GoWave Number for Steady Two-dimensional Waves Formula

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Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance. Check FAQs

k = (\frac{{ω c}^{2} \cdot d}{[g]}) \cdot \frac{1 - \exp (- {(ω c \cdot {\sqrt{\frac{d}{[g]}}}^{\frac{5}{2}})}^{- \frac{2}{5}})}{d}

k - Wave Number for Water Wave?ω_c - Angular Frequency of Wave?d - Coastal Mean Depth?[g] - Gravitational acceleration on Earth?[g] - Gravitational acceleration on Earth?

Guo Formula of Linear Dispersion Relation for Wave Number Example

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Here is how the Guo Formula of Linear Dispersion Relation for Wave Number equation looks like with Values.

Here is how the Guo Formula of Linear Dispersion Relation for Wave Number equation looks like with Units.

Here is how the Guo Formula of Linear Dispersion Relation for Wave Number equation looks like.

0.2228 = (\frac{{2.04}^{2} \cdot 10}{9.8066}) \cdot \frac{1 - \exp (- {(2.04 \cdot {\sqrt{\frac{10}{9.8066}}}^{\frac{5}{2}})}^{- \frac{2}{5}})}{10}

0.2228 = (\frac{{2.04rad/s}^{2} \cdot 10m}{9.8066m/s²}) \cdot \frac{1 - \exp (- {(2.04rad/s \cdot {\sqrt{\frac{10m}{9.8066m/s²}}}^{\frac{5}{2}})}^{- \frac{2}{5}})}{10m}

0.2228 = (\frac{{2.04}^{2} \cdot 10}{9.8066}) \cdot \frac{1 - \exp (- {(2.04 \cdot {\sqrt{\frac{10}{9.8066}}}^{\frac{5}{2}})}^{- \frac{2}{5}})}{10}

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Guo Formula of Linear Dispersion Relation for Wave Number Solution

Follow our step by step solution on how to calculate Guo Formula of Linear Dispersion Relation for Wave Number?

FIRST Step Consider the formula

k = (\frac{{ω c}^{2} \cdot d}{[g]}) \cdot \frac{1 - \exp (- {(ω c \cdot {\sqrt{\frac{d}{[g]}}}^{\frac{5}{2}})}^{- \frac{2}{5}})}{d}

Next Step Substitute values of Variables

∴

k = (\frac{{2.04rad/s}^{2} \cdot 10m}{[g]}) \cdot \frac{1 - \exp (- {(2.04rad/s \cdot {\sqrt{\frac{10m}{[g]}}}^{\frac{5}{2}})}^{- \frac{2}{5}})}{10m}

Next Step Substitute values of Constants

∴

k = (\frac{{2.04rad/s}^{2} \cdot 10m}{9.8066m/s²}) \cdot \frac{1 - \exp (- {(2.04rad/s \cdot {\sqrt{\frac{10m}{9.8066m/s²}}}^{\frac{5}{2}})}^{- \frac{2}{5}})}{10m}

Next Step Prepare to Evaluate

∴

k = (\frac{{2.04}^{2} \cdot 10}{9.8066}) \cdot \frac{1 - \exp (- {(2.04 \cdot {\sqrt{\frac{10}{9.8066}}}^{\frac{5}{2}})}^{- \frac{2}{5}})}{10}

Next Step Evaluate

∴

k = 0.222818729954921

LAST Step Rounding Answer

∴

k = 0.2228

Guo Formula of Linear Dispersion Relation for Wave Number Formula Elements

Variables

Constants

Functions

Wave Number for Water Wave

Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wave Number for Water Wave

Angular Frequency of Wave

Angular Frequency of Wave is the rate of change of phase of a sinusoidal waveform, typically measured in radians per second.

Symbol: ω_c

Measurement: Angular FrequencyUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Frequency of Wave

Coastal Mean Depth

Coastal Mean Depth of a fluid flow is a measure of the average depth of the fluid in a channel, pipe, or other conduit through which the fluid is flowing.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Coastal Mean Depth

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

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)

Other Formulas to find Wave Number for Water Wave

Go Wave Number of Convenient Empirical Explicit Approximation

k = (\frac{{ω c}^{2}}{[g]}) \cdot (\coth ({(ω c \cdot {\sqrt{\frac{d}{[g]}}}^{\frac{3}{2}})}^{\frac{2}{3}}))

Go Wave Number for Steady Two-dimensional Waves

k = \frac{2 \cdot π}{λ''}

Other formulas in Linear Dispersion Relation of Linear Wave category

Go Velocity of Propagation in Linear Dispersion Relation

C v = \sqrt{\frac{[g] \cdot d \cdot \tanh (k \cdot d)}{k \cdot d}}

Go Wavelength given Wave Number

λ'' = \frac{2 \cdot π}{k}

Go Relative Wavelength

λ r = \frac{λ o}{d}

Go Velocity of Propagation in Linear Dispersion Relation given Wavelength

C v = \sqrt{\frac{[g] \cdot d \cdot \tanh (2 \cdot π \cdot \frac{d}{λ''})}{2 \cdot π \cdot \frac{d}{λ''}}}

How to Evaluate Guo Formula of Linear Dispersion Relation for Wave Number?

Guo Formula of Linear Dispersion Relation for Wave Number evaluator uses Wave Number for Water Wave = ((Angular Frequency of Wave^2*Coastal Mean Depth)/[g])*(1-exp(-(Angular Frequency of Wave*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5)))/Coastal Mean Depth to evaluate the Wave Number for Water Wave, The Guo Formula of Linear Dispersion Relation for Wave Number is defined as the mechanism of swell waves propagation on the surface of a homogeneous fluid layer can be represented by a linear theory. Wave Number for Water Wave is denoted by k symbol.

How to evaluate Guo Formula of Linear Dispersion Relation for Wave Number using this online evaluator? To use this online evaluator for Guo Formula of Linear Dispersion Relation for Wave Number, enter Angular Frequency of Wave (ω_c) & Coastal Mean Depth (d) and hit the calculate button.

FAQs on Guo Formula of Linear Dispersion Relation for Wave Number

What is the formula to find Guo Formula of Linear Dispersion Relation for Wave Number?

The formula of Guo Formula of Linear Dispersion Relation for Wave Number is expressed as Wave Number for Water Wave = ((Angular Frequency of Wave^2*Coastal Mean Depth)/[g])*(1-exp(-(Angular Frequency of Wave*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5)))/Coastal Mean Depth. Here is an example- 0.222819 = ((2.04^2*10)/[g])*(1-exp(-(2.04*sqrt(10/[g])^(5/2))^(-2/5)))/10.

How to calculate Guo Formula of Linear Dispersion Relation for Wave Number?

With Angular Frequency of Wave (ω_c) & Coastal Mean Depth (d) we can find Guo Formula of Linear Dispersion Relation for Wave Number using the formula - Wave Number for Water Wave = ((Angular Frequency of Wave^2*Coastal Mean Depth)/[g])*(1-exp(-(Angular Frequency of Wave*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5)))/Coastal Mean Depth. This formula also uses Gravitational acceleration on Earth, Gravitational acceleration on Earth constant(s) and , Exponential Growth (exp), Square Root (sqrt) function(s).

What are the other ways to Calculate Wave Number for Water Wave?

Here are the different ways to Calculate Wave Number for Water Wave-

Wave Number for Water Wave=(Angular Frequency of Wave^2/[g])*(coth((Angular Frequency of Wave*sqrt(Coastal Mean Depth/[g])^(3/2))^(2/3)))
Wave Number for Water Wave=(2*pi)/Deep Water Wavelength of Coast

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