Wave Number of Convenient Empirical Explicit Approximation Calculator

✖Angular Frequency of Wave is defined as the rate of change of phase of a sinusoidal waveform, typically measured in radians per second.ⓘ Angular Frequency of Wave [ω_c]			+10% -10%
✖Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.ⓘ Coastal Mean Depth [d]			+10% -10%

✖Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance.ⓘ Wave Number of Convenient Empirical Explicit Approximation [k]

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Wave Number of Convenient Empirical Explicit Approximation

Formula

`"k" = ("ω"_{"c"}^2/"[g]")*(coth(("ω"_{"c"}*sqrt("d"/"[g]")^(3/2))^(2/3)))`

Example

`"0.458653"=(("2.04rad/s")^2/"[g]")*(coth(("2.04rad/s"*sqrt("10m"/"[g]")^(3/2))^(2/3)))`

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Wave Number of Convenient Empirical Explicit Approximation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
k = (ω_c^2/[g])*(coth((ω_c*sqrt(d/[g])^(3/2))^(2/3)))
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

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

Variables Used

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.
Angular Frequency of Wave - (Measured in Radian per Second) - Angular Frequency of Wave is defined as the rate of change of phase of a sinusoidal waveform, typically measured in radians per second.
Coastal Mean Depth - (Measured in Meter) - Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.

STEP 1: Convert Input(s) to Base Unit

Angular Frequency of Wave: 2.04 Radian per Second --> 2.04 Radian per Second No Conversion Required
Coastal Mean Depth: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k = (ω_c^2/[g])*(coth((ω_c*sqrt(d/[g])^(3/2))^(2/3))) --> (2.04^2/[g])*(coth((2.04*sqrt(10/[g])^(3/2))^(2/3)))

Evaluating ... ...

k = 0.458653055363701

STEP 3: Convert Result to Output's Unit

0.458653055363701 --> No Conversion Required

FINAL ANSWER

0.458653055363701 ≈ 0.458653 <-- Wave Number for Water Wave

(Calculation completed in 00.020 seconds)

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< 12 Linear Dispersion Relation of Linear Wave Calculators

Velocity of Propagation in Linear Dispersion Relation given Wavelength

Go Velocity of Propagation = sqrt(([g]*Coastal Mean Depth*tanh(2*pi*Coastal Mean Depth/Deep Water Wavelength of Coast))/(2*pi*Coastal Mean Depth/Deep Water Wavelength of Coast))

Guo Formula of Linear Dispersion Relation for Wave Number

Go 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

Guo Formula of Linear Dispersion Relation

Go Linear Dispersion Relation = (Wave Angular Frequency^2*Coastal Mean Depth/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5)))

Velocity of Propagation in Linear Dispersion Relation

Go Velocity of Propagation = sqrt(([g]*Coastal Mean Depth*tanh(Wave Number for Water Wave*Coastal Mean Depth))/(Wave Number for Water Wave*Coastal Mean Depth))

Wave Number of Convenient Empirical Explicit Approximation

Go 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)))

Radian Frequency of Wave

Go Angular Frequency of Wave = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Coastal Mean Depth))

Dimensionless Wave Speed

Go Wave Speed = Propagation Velocity/sqrt([g]*Coastal Mean Depth)

Wave Number for Steady Two-dimensional Waves

Go Wave Number for Water Wave = (2*pi)/Deep Water Wavelength of Coast

Wavelength given Wave Number

Go Deep Water Wavelength of Coast = (2*pi)/Wave Number for Water Wave

Relative Wavelength

Go Relative Wavelength = Deep-Water Wavelength/Coastal Mean Depth

Wave period given Radian Frequency of Waves

Go Wave Period = 2*pi/Wave Angular Frequency

Radian Frequency of Waves

Go Wave Angular Frequency = 2*pi/Wave Period

Wave Number of Convenient Empirical Explicit Approximation 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)))
k = (ω_c^2/[g])*(coth((ω_c*sqrt(d/[g])^(3/2))^(2/3)))

What is Wave Period?

The wave period is the time it takes to complete one cycle. The standard unit of a wave period is in seconds, and it is inversely proportional to the frequency of a wave, which is the number of cycles of waves that occur in one second. In other words, the higher the frequency of a wave, the lower the wave period.

How to Calculate Wave Number of Convenient Empirical Explicit Approximation?

Wave Number of Convenient Empirical Explicit Approximation calculator 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 calculate 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 calculate Wave Number of Convenient Empirical Explicit Approximation using this online calculator? To use this online calculator for Wave Number of Convenient Empirical Explicit Approximation, enter Angular Frequency of Wave (ω_c) & Coastal Mean Depth (d) and hit the calculate button. Here is how the Wave Number of Convenient Empirical Explicit Approximation calculation can be explained with given input values -> 0.458653 = (2.04^2/[g])*(coth((2.04*sqrt(10/[g])^(3/2))^(2/3))).

FAQ

What is Wave Number of Convenient Empirical Explicit Approximation?

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 and is represented as k = (ω_c^2/[g])*(coth((ω_c*sqrt(d/[g])^(3/2))^(2/3))) or 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))). Angular Frequency of Wave is defined as the rate of change of phase of a sinusoidal waveform, typically measured in radians per second & Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.

How to calculate Wave Number of Convenient Empirical Explicit Approximation?

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 is calculated using 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 calculate Wave Number of Convenient Empirical Explicit Approximation, you need Angular Frequency of Wave (ω_c) & Coastal Mean Depth (d). With our tool, you need to enter the respective value for Angular Frequency of Wave & Coastal Mean Depth and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Wave Number for Water Wave?

In this formula, Wave Number for Water Wave uses Angular Frequency of Wave & Coastal Mean Depth. We can use 2 other way(s) to calculate the same, which is/are as follows -

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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