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Group Velocity of Waves Formula

GoGroup Velocity given Wave Power per unit Crest Width Formula

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The Group Velocity of Waves refers to the velocity at which the overall shape or envelope of a wave group propagates through a medium. Check FAQs

V g = 0.5 \cdot v \cdot (1 + (\frac{k \cdot d}{\sinh (k \cdot d) \cdot \cosh (k \cdot d)}))

V_g - Group Velocity of Waves?v - Wave Speed?k - Wave Number for Water Wave?d - Coastal Mean Depth?

Group Velocity of Waves Example

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Here is how the Group Velocity of Waves equation looks like with Values.

Here is how the Group Velocity of Waves equation looks like with Units.

Here is how the Group Velocity of Waves equation looks like.

28.6644 = 0.5 \cdot 50 \cdot (1 + (\frac{0.2 \cdot 10}{\sinh (0.2 \cdot 10) \cdot \cosh (0.2 \cdot 10)}))

28.6644m/s = 0.5 \cdot 50m/s \cdot (1 + (\frac{0.2 \cdot 10m}{\sinh (0.2 \cdot 10m) \cdot \cosh (0.2 \cdot 10m)}))

28.6644 = 0.5 \cdot 50 \cdot (1 + (\frac{0.2 \cdot 10}{\sinh (0.2 \cdot 10) \cdot \cosh (0.2 \cdot 10)}))

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Group Velocity of Waves Solution

Follow our step by step solution on how to calculate Group Velocity of Waves?

FIRST Step Consider the formula

V g = 0.5 \cdot v \cdot (1 + (\frac{k \cdot d}{\sinh (k \cdot d) \cdot \cosh (k \cdot d)}))

Next Step Substitute values of Variables

∴

V g = 0.5 \cdot 50m/s \cdot (1 + (\frac{0.2 \cdot 10m}{\sinh (0.2 \cdot 10m) \cdot \cosh (0.2 \cdot 10m)}))

Next Step Prepare to Evaluate

∴

V g = 0.5 \cdot 50 \cdot (1 + (\frac{0.2 \cdot 10}{\sinh (0.2 \cdot 10) \cdot \cosh (0.2 \cdot 10)}))

Next Step Evaluate

∴

V g = 28.6643570325866m/s

LAST Step Rounding Answer

∴

V g = 28.6644m/s

Group Velocity of Waves Formula Elements

Variables

Functions

Group Velocity of Waves

The Group Velocity of Waves refers to the velocity at which the overall shape or envelope of a wave group propagates through a medium.

Symbol: V_g

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Group Velocity of Waves

Wave Speed

Wave Speed is the rate at which a wave travels through a medium, measured in distance per unit time.

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Wave Speed

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

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

sinh

The hyperbolic sine function, also known as the sinh function, is a mathematical function that is defined as the hyperbolic analogue of the sine function.

Syntax: sinh(Number)

cosh

The hyperbolic cosine function is a mathematical function that is defined as the ratio of the sum of the exponential functions of x and negative x to 2.

Syntax: cosh(Number)

Other Formulas to find Group Velocity of Waves

Go Group Velocity given Wave Power per unit Crest Width

V g = \frac{P}{E}

Other formulas in Group Velocity, Beats, Energy Transport category

Go Wave Power per unit Crest Width

P = E \cdot V g

Go Total Energy per unit Area given Wave Power per unit Crest Width

E = \frac{P}{V g}

Go Wave Speed

v = \frac{ω}{k''}

Go Radian Frequency given Wave Propagation

ω = k \cdot x

How to Evaluate Group Velocity of Waves?

Group Velocity of Waves evaluator uses Group Velocity of Waves = 0.5*Wave Speed*(1+((Wave Number for Water Wave*Coastal Mean Depth)/(sinh(Wave Number for Water Wave*Coastal Mean Depth)*cosh(Wave Number for Water Wave*Coastal Mean Depth)))) to evaluate the Group Velocity of Waves, The Group Velocity of Waves formula is defined as the velocity with which the overall envelope shape of the wave's amplitudes known as the modulation or envelope of the wave propagates through space. Group Velocity of Waves is denoted by V_g symbol.

How to evaluate Group Velocity of Waves using this online evaluator? To use this online evaluator for Group Velocity of Waves, enter Wave Speed (v), Wave Number for Water Wave (k) & Coastal Mean Depth (d) and hit the calculate button.

FAQs on Group Velocity of Waves

What is the formula to find Group Velocity of Waves?

The formula of Group Velocity of Waves is expressed as Group Velocity of Waves = 0.5*Wave Speed*(1+((Wave Number for Water Wave*Coastal Mean Depth)/(sinh(Wave Number for Water Wave*Coastal Mean Depth)*cosh(Wave Number for Water Wave*Coastal Mean Depth)))). Here is an example- 28.66436 = 0.5*50*(1+((0.2*10)/(sinh(0.2*10)*cosh(0.2*10)))).

How to calculate Group Velocity of Waves?

With Wave Speed (v), Wave Number for Water Wave (k) & Coastal Mean Depth (d) we can find Group Velocity of Waves using the formula - Group Velocity of Waves = 0.5*Wave Speed*(1+((Wave Number for Water Wave*Coastal Mean Depth)/(sinh(Wave Number for Water Wave*Coastal Mean Depth)*cosh(Wave Number for Water Wave*Coastal Mean Depth)))). This formula also uses Hyperbolic Sine (sinh), Hyperbolic Cosine (cosh) function(s).

What are the other ways to Calculate Group Velocity of Waves?

Here are the different ways to Calculate Group Velocity of Waves-

Group Velocity of Waves=Wave Power Per Unit Crest Width/Total Energy Per Unit Area

Can the Group Velocity of Waves be negative?

No, the Group Velocity of Waves, measured in Speed cannot be negative.

Which unit is used to measure Group Velocity of Waves?

Group Velocity of Waves 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 Group Velocity of Waves can be measured.

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