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Wave Phase Velocity Formula

GoWave Phase Velocity for Wavelength and Wave Period Formula

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Wave Phase Velocity is the speed at which a wave crest or trough moves through the water. It is defined as the distance a wave crest travels per unit of time. Check FAQs

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

C_v - Wave Phase Velocity?k - Wave Number for Water Wave?D - Water Depth of Coast?[g] - Gravitational acceleration on Earth?

Wave Phase Velocity Example

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Here is how the Wave Phase Velocity equation looks like with Values.

Here is how the Wave Phase Velocity equation looks like with Units.

Here is how the Wave Phase Velocity equation looks like.

6.945 = \sqrt{(\frac{9.8066}{0.2}) \cdot \tanh (0.2 \cdot 12)}

6.945m/s = \sqrt{(\frac{9.8066m/s²}{0.2}) \cdot \tanh (0.2 \cdot 12m)}

6.945 = \sqrt{(\frac{9.8066}{0.2}) \cdot \tanh (0.2 \cdot 12)}

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Wave Phase Velocity Solution

Follow our step by step solution on how to calculate Wave Phase Velocity?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

C v = \sqrt{(\frac{[g]}{0.2}) \cdot \tanh (0.2 \cdot 12m)}

Next Step Substitute values of Constants

∴

C v = \sqrt{(\frac{9.8066m/s²}{0.2}) \cdot \tanh (0.2 \cdot 12m)}

Next Step Prepare to Evaluate

∴

C v = \sqrt{(\frac{9.8066}{0.2}) \cdot \tanh (0.2 \cdot 12)}

Next Step Evaluate

∴

C v = 6.94498201696798m/s

LAST Step Rounding Answer

∴

C v = 6.945m/s

Wave Phase Velocity Formula Elements

Variables

Constants

Functions

Wave Phase Velocity

Wave Phase Velocity is the speed at which a wave crest or trough moves through the water. It is defined as the distance a wave crest travels per unit of time.

Symbol: C_v

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Wave Phase Velocity

Wave Number for Water Wave

Wave Number for Water Wave is the spatial frequency of the wave, representing the number of wave cycles per unit distance. Understanding the wave number is crucial for designing seawalls etc.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wave Number for Water Wave

Water Depth of Coast

Water Depth of Coast is the measurement of the distance from the ocean surface to the seabed in coastal areas. It varies from shallow depths near the shore to deeper areas offshore.

Symbol: D

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth 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

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 Wave Phase Velocity

Go Wave Phase Velocity for Wavelength and Wave Period

C v = \frac{λ}{T'}

Other formulas in Wave Power category

Go Power per unit Crest Length

P = E \cdot C G

Go Wave Energy for Power per unit Crest Length

E = \frac{P}{C G}

Go Group Wave Celerity for Power per unit Crest Length

C G = \frac{P}{E}

Go Power per unit Crest Length given Ratio of Group Velocity to Phase Velocity

P = E \cdot n \cdot C

How to Evaluate Wave Phase Velocity?

Wave Phase Velocity evaluator uses Wave Phase Velocity = sqrt(([g]/Wave Number for Water Wave)*tanh(Wave Number for Water Wave*Water Depth of Coast)) to evaluate the Wave Phase Velocity, The Wave Phase Velocity Formula is defined as the speed at which a specific phase of a wave propagates through a medium. In coastal engineering, understanding wave phase velocity is crucial for various reasons. Firstly, it helps in predicting the movement of waves as they approach and interact with coastal structures such as breakwaters, seawalls, and harbors. By knowing the phase velocity, engineers can design these structures to withstand the forces exerted by waves effectively. Wave Phase Velocity is denoted by C_v symbol.

How to evaluate Wave Phase Velocity using this online evaluator? To use this online evaluator for Wave Phase Velocity, enter Wave Number for Water Wave (k) & Water Depth of Coast (D) and hit the calculate button.

FAQs on Wave Phase Velocity

What is the formula to find Wave Phase Velocity?

The formula of Wave Phase Velocity is expressed as Wave Phase Velocity = sqrt(([g]/Wave Number for Water Wave)*tanh(Wave Number for Water Wave*Water Depth of Coast)). Here is an example- 6.944982 = sqrt(([g]/0.2)*tanh(0.2*12)).

How to calculate Wave Phase Velocity?

With Wave Number for Water Wave (k) & Water Depth of Coast (D) we can find Wave Phase Velocity using the formula - Wave Phase Velocity = sqrt(([g]/Wave Number for Water Wave)*tanh(Wave Number for Water Wave*Water Depth of Coast)). 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 Wave Phase Velocity?

Here are the different ways to Calculate Wave Phase Velocity-

Wave Phase Velocity=Wavelength/Mean Wave Period

Can the Wave Phase Velocity be negative?

No, the Wave Phase Velocity, measured in Speed cannot be negative.

Which unit is used to measure Wave Phase Velocity?

Wave Phase Velocity 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 Wave Phase Velocity can be measured.

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Wave Phase Velocity Formula

​GoWave Phase Velocity for Wavelength and Wave Period Formula

Wave Phase Velocity Example

Wave Phase Velocity Solution

Wave Phase Velocity Formula Elements

Other Formulas to find Wave Phase Velocity

Other formulas in Wave Power category

How to Evaluate Wave Phase Velocity?

FAQs on Wave Phase Velocity

Variable Name

GoWave Phase Velocity for Wavelength and Wave Period Formula