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Wave Number of Convenient Empirical Explicit Approximation Formula

GoGuo Formula of Linear Dispersion Relation for Wave Number 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}}{[g]}) \cdot (\coth ({(ω c \cdot {\sqrt{\frac{d}{[g]}}}^{\frac{3}{2}})}^{\frac{2}{3}}))

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?

Wave Number of Convenient Empirical Explicit Approximation Example

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Here is how the Wave Number of Convenient Empirical Explicit Approximation equation looks like.

0.4587 = (\frac{{2.04}^{2}}{9.8066}) \cdot (\coth ({(2.04 \cdot {\sqrt{\frac{10}{9.8066}}}^{\frac{3}{2}})}^{\frac{2}{3}}))

0.4587 = (\frac{{2.04rad/s}^{2}}{9.8066m/s²}) \cdot (\coth ({(2.04rad/s \cdot {\sqrt{\frac{10m}{9.8066m/s²}}}^{\frac{3}{2}})}^{\frac{2}{3}}))

0.4587 = (\frac{{2.04}^{2}}{9.8066}) \cdot (\coth ({(2.04 \cdot {\sqrt{\frac{10}{9.8066}}}^{\frac{3}{2}})}^{\frac{2}{3}}))

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Wave Number of Convenient Empirical Explicit Approximation Solution

Follow our step by step solution on how to calculate Wave Number of Convenient Empirical Explicit Approximation?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

k = (\frac{{2.04rad/s}^{2}}{[g]}) \cdot (\coth ({(2.04rad/s \cdot {\sqrt{\frac{10m}{[g]}}}^{\frac{3}{2}})}^{\frac{2}{3}}))

Next Step Substitute values of Constants

∴

k = (\frac{{2.04rad/s}^{2}}{9.8066m/s²}) \cdot (\coth ({(2.04rad/s \cdot {\sqrt{\frac{10m}{9.8066m/s²}}}^{\frac{3}{2}})}^{\frac{2}{3}}))

Next Step Prepare to Evaluate

∴

k = (\frac{{2.04}^{2}}{9.8066}) \cdot (\coth ({(2.04 \cdot {\sqrt{\frac{10}{9.8066}}}^{\frac{3}{2}})}^{\frac{2}{3}}))

Next Step Evaluate

∴

k = 0.458653055363701

LAST Step Rounding Answer

∴

k = 0.4587

Wave Number of Convenient Empirical Explicit Approximation 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

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)

coth

The hyperbolic cotangent function, denoted as coth(x), is defined as the ratio of the hyperbolic cosine to the hyperbolic sine.

Syntax: coth(Number)

Other Formulas to find Wave Number for Water Wave

Go Guo Formula of Linear Dispersion Relation for Wave Number

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}

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 Wave Number of Convenient Empirical Explicit Approximation?

Wave Number of Convenient Empirical Explicit Approximation evaluator uses 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))) to evaluate the Wave Number for Water Wave, The Wave Number of Convenient Empirical Explicit Approximation is defined as the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Wave Number for Water Wave is denoted by k symbol.

How to evaluate Wave Number of Convenient Empirical Explicit Approximation using this online evaluator? To use this online evaluator for Wave Number of Convenient Empirical Explicit Approximation, enter Angular Frequency of Wave (ω_c) & Coastal Mean Depth (d) and hit the calculate button.

FAQs on Wave Number of Convenient Empirical Explicit Approximation

What is the formula to find Wave Number of Convenient Empirical Explicit Approximation?

The formula of Wave Number of Convenient Empirical Explicit Approximation is expressed as 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))). Here is an example- 0.458653 = (2.04^2/[g])*(coth((2.04*sqrt(10/[g])^(3/2))^(2/3))).

How to calculate Wave Number of Convenient Empirical Explicit Approximation?

With Angular Frequency of Wave (ω_c) & Coastal Mean Depth (d) we can find Wave Number of Convenient Empirical Explicit Approximation using the formula - 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))). This formula also uses Gravitational acceleration on Earth, Gravitational acceleration on Earth constant(s) and , Square Root Function, hyperbolic cotangent 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*Coastal Mean Depth)/[g])*(1-exp(-(Angular Frequency of Wave*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5)))/Coastal Mean Depth
Wave Number for Water Wave=(2*pi)/Deep Water Wavelength of Coast

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