Velocity of Propagation in Linear Dispersion Relation given Wavelength Calculator

✖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.ⓘ 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 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 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.
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: 31.4 Meter --> 31.4 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*10/31.4))/(2*pi*10/31.4))

Evaluating ... ...

C_v = 6.87378722230857

STEP 3: Convert Result to Output's Unit

6.87378722230857 Meter per Second --> No Conversion Required

FINAL ANSWER

6.87378722230857 ≈ 6.873787 Meter per Second <-- Velocity of Propagation

(Calculation completed in 00.009 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< Linear Dispersion Relation of Linear Wave Calculators

Velocity of Propagation in Linear Dispersion Relation given Wavelength

LaTeX 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))

Velocity of Propagation in Linear Dispersion Relation

LaTeX 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))

Wavelength given Wave Number

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

Relative Wavelength

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

Velocity of Propagation in Linear Dispersion Relation given Wavelength Formula

LaTeX Go

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 speed at which a wave travels through a medium, indicating the rate of energy transfer, calculated using wavelength. 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*10/31.4))/(2*pi*10/31.4)).

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 speed at which a wave travels through a medium, indicating the rate of energy transfer, calculated using wavelength 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 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 & 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 speed at which a wave travels through a medium, indicating the rate of energy transfer, calculated using wavelength 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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