Velocity of Propagation in Linear Dispersion Relation Calculator

✖Coastal Mean Depth is the average water depth 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 for Water Wave [k]			+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 [C_v]

⎘ Copy

👎

Formula

✖

Velocity of Propagation in Linear Dispersion Relation

Formula

`"C"_{"v"} = sqrt(("[g]"*"d"*tanh("k"*"d"))/("k"*"d"))`

Example

`"6.875275m/s"=sqrt(("[g]"*"10m"*tanh("0.2"*"10m"))/("0.2"*"10m"))`

Calculator

LaTeX

Reset

👍

Download Coastal and Ocean Engineering Formula PDF PDF Image

Velocity of Propagation in Linear Dispersion Relation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
C_v = sqrt(([g]*d*tanh(k*d))/(k*d))
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)
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 is the average water depth over a particular area, such as a section of coastline, a bay, or an ocean basin.
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.

STEP 1: Convert Input(s) to Base Unit

Coastal Mean Depth: 10 Meter --> 10 Meter No Conversion Required
Wave Number for Water Wave: 0.2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_v = sqrt(([g]*d*tanh(k*d))/(k*d)) --> sqrt(([g]*10*tanh(0.2*10))/(0.2*10))

Evaluating ... ...

C_v = 6.87527492837578

STEP 3: Convert Result to Output's Unit

6.87527492837578 Meter per Second --> No Conversion Required

FINAL ANSWER

6.87527492837578 ≈ 6.875275 Meter per Second <-- Velocity of Propagation

(Calculation completed in 00.004 seconds)

You are here -

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

Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Calculator and 1700+ more calculators!

< 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 Formula

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))
C_v = sqrt(([g]*d*tanh(k*d))/(k*d))

What is Viscosity?

The Viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.

How to Calculate Velocity of Propagation in Linear Dispersion Relation?

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

How to calculate Velocity of Propagation in Linear Dispersion Relation using this online calculator? To use this online calculator for Velocity of Propagation in Linear Dispersion Relation, enter Coastal Mean Depth (d) & Wave Number for Water Wave (k) and hit the calculate button. Here is how the Velocity of Propagation in Linear Dispersion Relation calculation can be explained with given input values -> 6.875275 = sqrt(([g]*10*tanh(0.2*10))/(0.2*10)).

FAQ

What is Velocity of Propagation in Linear Dispersion Relation?

The Velocity of Propagation in Linear Dispersion Relation is defined as the change of its position with respect to a frame of reference of waves travel with respect to the direction of the oscillation relative to the propagation direction and is represented as C_v = sqrt(([g]*d*tanh(k*d))/(k*d)) or 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)). Coastal Mean Depth is the average water depth over a particular area, such as a section of coastline, a bay, or an ocean basin & Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance.

How to calculate Velocity of Propagation in Linear Dispersion Relation?

The Velocity of Propagation in Linear Dispersion Relation is defined as the change of its position with respect to a frame of reference of waves travel with respect to the direction of the oscillation relative to the propagation direction is calculated using 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)). To calculate Velocity of Propagation in Linear Dispersion Relation, you need Coastal Mean Depth (d) & Wave Number for Water Wave (k). With our tool, you need to enter the respective value for Coastal Mean Depth & Wave Number for Water Wave 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 & Wave Number for Water Wave. 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(2*pi*Coastal Mean Depth/Deep Water Wavelength of Coast))/(2*pi*Coastal Mean Depth/Deep Water Wavelength of Coast))

Home

FREE PDFs

🔍 Search