Guo Formula of Linear Dispersion Relation for Wave Number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Wave Number for Water Wave = ((Wave Angular Frequency^2*Mean Depth)/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Mean Depth/[g])^(5/2))^(-2/5)))/Mean Depth
k = ((ω^2*d)/[g])*(1-exp(-(ω*sqrt(d/[g])^(5/2))^(-2/5)))/d
This formula uses 1 Constants, 2 Functions, 3 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
Functions Used
exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., 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., sqrt(Number)
Variables Used
Wave Number for Water Wave - The wave number for water waves quantifies the number of waves per unit length along the surface of the water.
Wave Angular Frequency - (Measured in Radian per Second) - Wave Angular Frequency angular displacement of the wave per unit time. Its units are therefore degrees (or radians) per second.
Mean Depth - (Measured in Meter) - Mean Depth for Steady two-dimensional waves.
STEP 1: Convert Input(s) to Base Unit
Wave Angular Frequency: 6.2 Radian per Second --> 6.2 Radian per Second No Conversion Required
Mean Depth: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
k = ((ω^2*d)/[g])*(1-exp(-(ω*sqrt(d/[g])^(5/2))^(-2/5)))/d --> ((6.2^2*10)/[g])*(1-exp(-(6.2*sqrt(10/[g])^(5/2))^(-2/5)))/10
Evaluating ... ...
k = 1.48776369750258
STEP 3: Convert Result to Output's Unit
1.48776369750258 --> No Conversion Required
FINAL ANSWER
1.48776369750258 1.487764 <-- Wave Number for Water Wave
(Calculation completed in 00.004 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]*Mean Depth*tanh(2*pi*Mean Depth/Deep-Water Wavelength))/(2*pi*Mean Depth/Deep-Water Wavelength))
Guo Formula of Linear Dispersion Relation for Wave Number
Go Wave Number for Water Wave = ((Wave Angular Frequency^2*Mean Depth)/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Mean Depth/[g])^(5/2))^(-2/5)))/Mean Depth
Guo Formula of Linear Dispersion Relation
Go Linear Dispersion Relation = (Wave Angular Frequency^2*Mean Depth/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Mean Depth/[g])^(5/2))^(-2/5)))
Velocity of Propagation in Linear Dispersion Relation
Go Velocity of Propagation = sqrt(([g]*Mean Depth*tanh(Wave Number for Water Wave*Mean Depth))/(Wave Number for Water Wave*Mean Depth))
Wave Number of Convenient Empirical Explicit Approximation
Go Wave Number for Water Wave = (Wave Angular Frequency^2/[g])*(coth((Wave Angular Frequency*sqrt(Mean Depth/[g])^(3/2))^(2/3)))
Radian Frequency of Wave
Go Wave Angular Frequency = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Mean Depth))
Dimensionless Wave Speed
Go Wave Speed = Velocity of Propagation/sqrt([g]*Mean Depth)
Wave Number for Steady Two-dimensional Waves
Go Wave Number for Water Wave = (2*pi)/Deep-Water Wavelength
Wavelength given wave number
Go Deep-Water Wavelength = (2*pi)/Wave Number for Water Wave
Relative Wavelength
Go Relative Wavelength = Deep-Water Wavelength/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

Guo Formula of Linear Dispersion Relation for Wave Number Formula

Wave Number for Water Wave = ((Wave Angular Frequency^2*Mean Depth)/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Mean Depth/[g])^(5/2))^(-2/5)))/Mean Depth
k = ((ω^2*d)/[g])*(1-exp(-(ω*sqrt(d/[g])^(5/2))^(-2/5)))/d

What is Wave Number?

The Wave Number is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance

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

Guo Formula of Linear Dispersion Relation for Wave Number calculator uses Wave Number for Water Wave = ((Wave Angular Frequency^2*Mean Depth)/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Mean Depth/[g])^(5/2))^(-2/5)))/Mean Depth to calculate the Wave Number for Water Wave, Guo Formula of Linear Dispersion Relation for Wave Number is based on the linear wave theory. When the assumption of small amplitude waves is made, 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 calculate Guo Formula of Linear Dispersion Relation for Wave Number using this online calculator? To use this online calculator for Guo Formula of Linear Dispersion Relation for Wave Number, enter Wave Angular Frequency (ω) & Mean Depth (d) and hit the calculate button. Here is how the Guo Formula of Linear Dispersion Relation for Wave Number calculation can be explained with given input values -> 1.487764 = ((6.2^2*10)/[g])*(1-exp(-(6.2*sqrt(10/[g])^(5/2))^(-2/5)))/10.

FAQ

What is Guo Formula of Linear Dispersion Relation for Wave Number?
Guo Formula of Linear Dispersion Relation for Wave Number is based on the linear wave theory. When the assumption of small amplitude waves is made, the mechanism of swell waves propagation on the surface of a homogeneous fluid layer can be represented by a linear theory and is represented as k = ((ω^2*d)/[g])*(1-exp(-(ω*sqrt(d/[g])^(5/2))^(-2/5)))/d or Wave Number for Water Wave = ((Wave Angular Frequency^2*Mean Depth)/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Mean Depth/[g])^(5/2))^(-2/5)))/Mean Depth. Wave Angular Frequency angular displacement of the wave per unit time. Its units are therefore degrees (or radians) per second & Mean Depth for Steady two-dimensional waves.
How to calculate Guo Formula of Linear Dispersion Relation for Wave Number?
Guo Formula of Linear Dispersion Relation for Wave Number is based on the linear wave theory. When the assumption of small amplitude waves is made, the mechanism of swell waves propagation on the surface of a homogeneous fluid layer can be represented by a linear theory is calculated using Wave Number for Water Wave = ((Wave Angular Frequency^2*Mean Depth)/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Mean Depth/[g])^(5/2))^(-2/5)))/Mean Depth. To calculate Guo Formula of Linear Dispersion Relation for Wave Number, you need Wave Angular Frequency (ω) & Mean Depth (d). With our tool, you need to enter the respective value for Wave Angular Frequency & 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 Wave Angular Frequency & Mean Depth. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Wave Number for Water Wave = (Wave Angular Frequency^2/[g])*(coth((Wave Angular Frequency*sqrt(Mean Depth/[g])^(3/2))^(2/3)))
  • Wave Number for Water Wave = (2*pi)/Deep-Water Wavelength
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