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Velocity of Propagation in Linear Dispersion Relation Formula

GoVelocity of Propagation in Linear Dispersion Relation given Wavelength Formula

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The Velocity of Propagation is the speed at which a wave travels through a medium, indicating the rate of energy transfer. Check FAQs

C v = \sqrt{\frac{[g] \cdot d \cdot \tanh (k \cdot d)}{k \cdot d}}

C_v - Velocity of Propagation?d - Coastal Mean Depth?k - Wave Number for Water Wave?[g] - Gravitational acceleration on Earth?

Velocity of Propagation in Linear Dispersion Relation Example

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Here is how the Velocity of Propagation in Linear Dispersion Relation equation looks like with Values.

Here is how the Velocity of Propagation in Linear Dispersion Relation equation looks like with Units.

Here is how the Velocity of Propagation in Linear Dispersion Relation equation looks like.

6.8753 = \sqrt{\frac{9.8066 \cdot 10 \cdot \tanh (0.2 \cdot 10)}{0.2 \cdot 10}}

6.8753m/s = \sqrt{\frac{9.8066m/s² \cdot 10m \cdot \tanh (0.2 \cdot 10m)}{0.2 \cdot 10m}}

6.8753 = \sqrt{\frac{9.8066 \cdot 10 \cdot \tanh (0.2 \cdot 10)}{0.2 \cdot 10}}

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Velocity of Propagation in Linear Dispersion Relation Solution

Follow our step by step solution on how to calculate Velocity of Propagation in Linear Dispersion Relation?

FIRST Step Consider the formula

C v = \sqrt{\frac{[g] \cdot d \cdot \tanh (k \cdot d)}{k \cdot d}}

Next Step Substitute values of Variables

∴

C v = \sqrt{\frac{[g] \cdot 10m \cdot \tanh (0.2 \cdot 10m)}{0.2 \cdot 10m}}

Next Step Substitute values of Constants

∴

C v = \sqrt{\frac{9.8066m/s² \cdot 10m \cdot \tanh (0.2 \cdot 10m)}{0.2 \cdot 10m}}

Next Step Prepare to Evaluate

∴

C v = \sqrt{\frac{9.8066 \cdot 10 \cdot \tanh (0.2 \cdot 10)}{0.2 \cdot 10}}

Next Step Evaluate

∴

C v = 6.87527492837578m/s

LAST Step Rounding Answer

∴

C v = 6.8753m/s

Velocity of Propagation in Linear Dispersion Relation Formula Elements

Variables

Constants

Functions

Velocity of Propagation

The Velocity of Propagation is the speed at which a wave travels through a medium, indicating the rate of energy transfer.

Symbol: C_v

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity of Propagation

Coastal Mean Depth

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.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Coastal Mean Depth

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.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wave Number for Water Wave

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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.

Syntax: 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).

Syntax: tanh(Number)

Other Formulas to find Velocity of Propagation

Go Velocity of Propagation in Linear Dispersion Relation given Wavelength

C v = \sqrt{\frac{[g] \cdot d \cdot \tanh (2 \cdot π \cdot \frac{d}{λ''})}{2 \cdot π \cdot \frac{d}{λ''}}}

Other formulas in Linear Dispersion Relation of Linear Wave category

Go Wavelength given Wave Number

λ'' = \frac{2 \cdot π}{k}

Go Relative Wavelength

λ r = \frac{λ o}{d}

Go Dimensionless Wave Speed

v = \frac{v p'}{\sqrt{[g] \cdot d}}

Go Radian Frequency of Waves

ω = 2 \cdot \frac{π}{T}

How to Evaluate Velocity of Propagation in Linear Dispersion Relation?

Velocity of Propagation in Linear Dispersion Relation evaluator 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 evaluate the Velocity of Propagation, The Velocity of Propagation in Linear Dispersion Relation is defined as the speed at which a wave travels through a medium, indicating the rate of energy transfer. Velocity of Propagation is denoted by C_v symbol.

How to evaluate Velocity of Propagation in Linear Dispersion Relation using this online evaluator? To use this online evaluator for Velocity of Propagation in Linear Dispersion Relation, enter Coastal Mean Depth (d) & Wave Number for Water Wave (k) and hit the calculate button.

FAQs on Velocity of Propagation in Linear Dispersion Relation

What is the formula to find Velocity of Propagation in Linear Dispersion Relation?

The formula of Velocity of Propagation in Linear Dispersion Relation is expressed as 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)). Here is an example- 6.875275 = sqrt(([g]*10*tanh(0.2*10))/(0.2*10)).

How to calculate Velocity of Propagation in Linear Dispersion Relation?

With Coastal Mean Depth (d) & Wave Number for Water Wave (k) we can find Velocity of Propagation in Linear Dispersion Relation using the 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)). This formula also uses Gravitational acceleration on Earth constant(s) and , Square Root (sqrt), Hyperbolic Tangent (tanh) function(s).

What are the other ways to Calculate Velocity of Propagation?

Here are the different ways to Calculate Velocity of Propagation-

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))

Can the Velocity of Propagation in Linear Dispersion Relation be negative?

Yes, the Velocity of Propagation in Linear Dispersion Relation, measured in Speed can be negative.

Which unit is used to measure Velocity of Propagation in Linear Dispersion Relation?

Velocity of Propagation in Linear Dispersion Relation is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Velocity of Propagation in Linear Dispersion Relation can be measured.

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