Velocity of Propagation in Linear Dispersion Relation given Wavelength Solution

STEP 0: Pre-Calculation Summary
Formula Used
Velocity of Propagation = sqrt(([g]*Mean Depth*tanh(2*pi*Mean Depth/Deep-Water Wavelength))/(2*pi*Mean Depth/Deep-Water Wavelength))
Cv = sqrt(([g]*d*tanh(2*pi*d/λo))/(2*pi*d/λo))
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.
Mean Depth - (Measured in Meter) - Mean Depth for Steady two-dimensional waves.
Deep-Water Wavelength - (Measured in Meter) - Deep-Water Wavelength, deep water waves are defined as those occurring in ocean depths greater than twice the wavelength of the wave.
STEP 1: Convert Input(s) to Base Unit
Mean Depth: 10 Meter --> 10 Meter No Conversion Required
Deep-Water Wavelength: 7 Meter --> 7 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Cv = sqrt(([g]*d*tanh(2*pi*d/λo))/(2*pi*d/λo)) --> sqrt(([g]*10*tanh(2*pi*10/7))/(2*pi*10/7))
Evaluating ... ...
Cv = 3.30536494347273
STEP 3: Convert Result to Output's Unit
3.30536494347273 Meter per Second --> No Conversion Required
FINAL ANSWER
3.30536494347273 3.305365 Meter per Second <-- Velocity of Propagation
(Calculation completed in 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg
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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

Velocity of Propagation in Linear Dispersion Relation given Wavelength Formula

Velocity of Propagation = sqrt(([g]*Mean Depth*tanh(2*pi*Mean Depth/Deep-Water Wavelength))/(2*pi*Mean Depth/Deep-Water Wavelength))
Cv = sqrt(([g]*d*tanh(2*pi*d/λo))/(2*pi*d/λo))

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]*Mean Depth*tanh(2*pi*Mean Depth/Deep-Water Wavelength))/(2*pi*Mean Depth/Deep-Water Wavelength)) to calculate the Velocity of Propagation, Velocity of Propagation in Linear Dispersion Relation given Wavelength referred to 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 Cv 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 Mean Depth (d) & Deep-Water Wavelength o) 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 -> 3.305365 = sqrt(([g]*10*tanh(2*pi*10/7))/(2*pi*10/7)).

FAQ

What is Velocity of Propagation in Linear Dispersion Relation given Wavelength?
Velocity of Propagation in Linear Dispersion Relation given Wavelength referred to 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 Cv = sqrt(([g]*d*tanh(2*pi*d/λo))/(2*pi*d/λo)) or Velocity of Propagation = sqrt(([g]*Mean Depth*tanh(2*pi*Mean Depth/Deep-Water Wavelength))/(2*pi*Mean Depth/Deep-Water Wavelength)). Mean Depth for Steady two-dimensional waves & Deep-Water Wavelength, deep water waves are defined as those occurring in ocean depths greater than twice the wavelength of the wave.
How to calculate Velocity of Propagation in Linear Dispersion Relation given Wavelength?
Velocity of Propagation in Linear Dispersion Relation given Wavelength referred to 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]*Mean Depth*tanh(2*pi*Mean Depth/Deep-Water Wavelength))/(2*pi*Mean Depth/Deep-Water Wavelength)). To calculate Velocity of Propagation in Linear Dispersion Relation given Wavelength, you need Mean Depth (d) & Deep-Water Wavelength o). With our tool, you need to enter the respective value for Mean Depth & Deep-Water Wavelength 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 Mean Depth & Deep-Water Wavelength. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Velocity of Propagation = sqrt(([g]*Mean Depth*tanh(Wave Number for Water Wave*Mean Depth))/(Wave Number for Water Wave*Mean Depth))
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