Velocity of Propagation in Linear Dispersion Relation given Wavelength Calculator

✖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%
✖Deep Water Wavelength of Coast refers to the wavelength of ocean waves as they propagate through water depths that are considered deep relative to the wave height.ⓘ Deep Water Wavelength of Coast [λ^'']			+10% -10%

✖The Velocity of Propagation is the speed at which a wave travels through a medium, indicating the rate of energy transfer.ⓘ Velocity of Propagation in Linear Dispersion Relation given Wavelength [C_v]

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Velocity of Propagation in Linear Dispersion Relation given Wavelength

Formula

`"C"_{"v"} = sqrt(("[g]"*"d"*tanh(2*pi*"d"/"λ"^{"''"}))/(2*pi*"d"/"λ"^{"''"}))`

Example

`"6.003073m/s"=sqrt(("[g]"*"10m"*tanh(2*pi*"10m"/"23.3m"))/(2*pi*"10m"/"23.3m"))`

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Velocity of Propagation in Linear Dispersion Relation given Wavelength Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
C_v = sqrt(([g]*d*tanh(2*pi*d/λ^''))/(2*pi*d/λ^''))
This formula uses 2 Constants, 2 Functions, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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)
tanh - The hyperbolic tangent function (tanh) is a function that is defined as the ratio of the hyperbolic sine function (sinh) to the hyperbolic cosine function (cosh)., tanh(Number)

Variables Used

Velocity of Propagation - (Measured in Meter per Second) - The Velocity of Propagation is the speed at which a wave travels through a medium, indicating the rate of energy transfer.
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.
Deep Water Wavelength of Coast - (Measured in Meter) - Deep Water Wavelength of Coast refers to the wavelength of ocean waves as they propagate through water depths that are considered deep relative to the wave height.

STEP 1: Convert Input(s) to Base Unit

Coastal Mean Depth: 10 Meter --> 10 Meter No Conversion Required
Deep Water Wavelength of Coast: 23.3 Meter --> 23.3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_v = sqrt(([g]*d*tanh(2*pi*d/λ^''))/(2*pi*d/λ^'')) --> sqrt(([g]*10*tanh(2*pi*10/23.3))/(2*pi*10/23.3))

Evaluating ... ...

C_v = 6.00307296960309

STEP 3: Convert Result to Output's Unit

6.00307296960309 Meter per Second --> No Conversion Required

FINAL ANSWER

6.00307296960309 ≈ 6.003073 Meter per Second <-- Velocity of Propagation

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surface Gravity Waves » Linear Dispersion Relation of Linear Wave » Velocity of Propagation in Linear Dispersion Relation given Wavelength

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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

Velocity of Propagation in Linear Dispersion Relation given Wavelength Formula

What is Wave Number?

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 Velocity of Propagation in Linear Dispersion Relation given Wavelength?

Velocity of Propagation in Linear Dispersion Relation given Wavelength calculator uses 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)) to calculate the Velocity of Propagation, The Velocity of Propagation in Linear Dispersion Relation given Wavelength is defined as the change of its position with respect to frame of reference of waves travel with respect to direction of oscillation relative to propagation direction. Velocity of Propagation is denoted by C_v symbol.

How to calculate Velocity of Propagation in Linear Dispersion Relation given Wavelength using this online calculator? To use this online calculator for Velocity of Propagation in Linear Dispersion Relation given Wavelength, enter Coastal Mean Depth (d) & Deep Water Wavelength of Coast (λ^'') and hit the calculate button. Here is how the Velocity of Propagation in Linear Dispersion Relation given Wavelength calculation can be explained with given input values -> 6.003073 = sqrt(([g]*10*tanh(2*pi*10/23.3))/(2*pi*10/23.3)).

FAQ

What is Velocity of Propagation in Linear Dispersion Relation given Wavelength?

The Velocity of Propagation in Linear Dispersion Relation given Wavelength is defined as the change of its position with respect to frame of reference of waves travel with respect to direction of oscillation relative to propagation direction and is represented as C_v = sqrt(([g]*d*tanh(2*pi*d/λ^''))/(2*pi*d/λ^'')) or 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)). 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 & Deep Water Wavelength of Coast refers to the wavelength of ocean waves as they propagate through water depths that are considered deep relative to the wave height.

How to calculate Velocity of Propagation in Linear Dispersion Relation given Wavelength?

The Velocity of Propagation in Linear Dispersion Relation given Wavelength is defined as the change of its position with respect to frame of reference of waves travel with respect to direction of oscillation relative to propagation direction is calculated using 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)). To calculate Velocity of Propagation in Linear Dispersion Relation given Wavelength, you need Coastal Mean Depth (d) & Deep Water Wavelength of Coast (λ^''). With our tool, you need to enter the respective value for Coastal Mean Depth & Deep Water Wavelength of Coast 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 Velocity of Propagation?

In this formula, Velocity of Propagation uses Coastal Mean Depth & Deep Water Wavelength of Coast. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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