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Velocity of Propagation in Linear Dispersion Relation given Wavelength Formula

GoVelocity of Propagation in Linear Dispersion Relation 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 (2 \cdot π \cdot \frac{d}{λ''})}{2 \cdot π \cdot \frac{d}{λ''}}}

C_v - Velocity of Propagation?d - Coastal Mean Depth?λ^'' - Deep Water Wavelength of Coast?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Velocity of Propagation in Linear Dispersion Relation given Wavelength Example

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

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

6.8738 = \sqrt{\frac{9.8066 \cdot 10 \cdot \tanh (2 \cdot 3.1416 \cdot \frac{10}{31.4})}{2 \cdot 3.1416 \cdot \frac{10}{31.4}}}

6.8738m/s = \sqrt{\frac{9.8066m/s² \cdot 10m \cdot \tanh (2 \cdot 3.1416 \cdot \frac{10m}{31.4m})}{2 \cdot 3.1416 \cdot \frac{10m}{31.4m}}}

6.8738 = \sqrt{\frac{9.8066 \cdot 10 \cdot \tanh (2 \cdot 3.1416 \cdot \frac{10}{31.4})}{2 \cdot 3.1416 \cdot \frac{10}{31.4}}}

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Velocity of Propagation in Linear Dispersion Relation given Wavelength Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

C v = \sqrt{\frac{[g] \cdot 10m \cdot \tanh (2 \cdot π \cdot \frac{10m}{31.4m})}{2 \cdot π \cdot \frac{10m}{31.4m}}}

Next Step Substitute values of Constants

∴

C v = \sqrt{\frac{9.8066m/s² \cdot 10m \cdot \tanh (2 \cdot 3.1416 \cdot \frac{10m}{31.4m})}{2 \cdot 3.1416 \cdot \frac{10m}{31.4m}}}

Next Step Prepare to Evaluate

∴

C v = \sqrt{\frac{9.8066 \cdot 10 \cdot \tanh (2 \cdot 3.1416 \cdot \frac{10}{31.4})}{2 \cdot 3.1416 \cdot \frac{10}{31.4}}}

Next Step Evaluate

∴

C v = 6.87378722230857m/s

LAST Step Rounding Answer

∴

C v = 6.8738m/s

Velocity of Propagation in Linear Dispersion Relation given Wavelength 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

Deep Water Wavelength of Coast

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.

Symbol: λ^''

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Deep Water Wavelength of Coast

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

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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

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

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 given Wavelength?

Velocity of Propagation in Linear Dispersion Relation given Wavelength evaluator 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 evaluate 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 evaluate Velocity of Propagation in Linear Dispersion Relation given Wavelength using this online evaluator? To use this online evaluator 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.

FAQs on Velocity of Propagation in Linear Dispersion Relation given Wavelength

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

The formula of Velocity of Propagation in Linear Dispersion Relation given Wavelength is expressed as 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)). Here is an example- 6.003073 = sqrt(([g]*10*tanh(2*pi*10/31.4))/(2*pi*10/31.4)).

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

With Coastal Mean Depth (d) & Deep Water Wavelength of Coast (λ^'') we can find Velocity of Propagation in Linear Dispersion Relation given Wavelength using the formula - 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)). This formula also uses Gravitational acceleration on Earth, Archimedes' constant 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(Wave Number for Water Wave*Coastal Mean Depth))/(Wave Number for Water Wave*Coastal Mean Depth))

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

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

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

Velocity of Propagation in Linear Dispersion Relation given Wavelength 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 given Wavelength can be measured.

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