Group Velocity of Waves Calculator

✖Wave Speed is the rate at which a wave travels through a medium, measured in distance per unit time.ⓘ Wave Speed [v]			+10% -10%
✖Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance.ⓘ Wave Number for Water Wave [k]			+10% -10%
✖Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.ⓘ Coastal Mean Depth [d]			+10% -10%

✖The Group Velocity of Waves is the velocity with which the overall envelope shape of the wave's amplitudes; known as the modulation.ⓘ Group Velocity of Waves [V_g]

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Formula

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Group Velocity of Waves

Formula

`"V"_{"g"} = 0.5*"v"*(1+(("k"*"d")/(sinh("k"*"d")*cosh("k"*"d"))))`

Example

`"28.66436m/s"=0.5*"50m/s"*(1+(("0.2"*"10m")/(sinh("0.2"*"10m")*cosh("0.2"*"10m"))))`

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Group Velocity of Waves Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
V_g = 0.5*v*(1+((k*d)/(sinh(k*d)*cosh(k*d))))
This formula uses 2 Functions, 4 Variables

Functions Used

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., 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., cosh(Number)

Variables Used

Group Velocity of Waves - (Measured in Meter per Second) - The Group Velocity of Waves is the velocity with which the overall envelope shape of the wave's amplitudes; known as the modulation.
Wave Speed - (Measured in Meter per Second) - Wave Speed is the rate at which a wave travels through a medium, measured in distance per unit time.
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.
Coastal Mean Depth - (Measured in Meter) - Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.

STEP 1: Convert Input(s) to Base Unit

Wave Speed: 50 Meter per Second --> 50 Meter per Second No Conversion Required
Wave Number for Water Wave: 0.2 --> No Conversion Required
Coastal Mean Depth: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_g = 0.5*v*(1+((k*d)/(sinh(k*d)*cosh(k*d)))) --> 0.5*50*(1+((0.2*10)/(sinh(0.2*10)*cosh(0.2*10))))

Evaluating ... ...

V_g = 28.6643570325866

STEP 3: Convert Result to Output's Unit

28.6643570325866 Meter per Second --> No Conversion Required

FINAL ANSWER

28.6643570325866 ≈ 28.66436 Meter per Second <-- Group Velocity of Waves

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surface Gravity Waves » Group Velocity, Beats, Energy Transport » Group Velocity of Waves

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

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< 9 Group Velocity, Beats, Energy Transport Calculators

Wave Speed given Group Velocity

Go Wave Speed = Group Velocity of Waves/(0.5*(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)))))

Group Velocity of Waves

Go 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))))

Surface Elevation

Go Surface Elevation = (Wave Height for Surface Gravity Waves/2)*cos((Wave Number for Water Wave*Propagation of Wave in One Direction)-(Wave Angular Frequency*Time))

Radian Frequency given Wave Propagation

Go Wave Angular Frequency = Wave Number for Water Wave*Propagation of Wave in One Direction

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

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

Group Velocity given Wave Power per unit Crest Width

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

Wave Power per unit Crest Width

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

Wavenumber given Wave Speed

Go Wave Number = Wave Angular Frequency/Wave Speed

Wave Speed

Go Wave Speed = Wave Angular Frequency/Wave Number

Group Velocity of Waves Formula

What is Wave Power and How does it Work?

Wave power is produced by the up and down motion of floating devices placed on the surface of the ocean. In other words, wind produces waves, and then waves produce energy. As the waves travel across the ocean, high-tech devices capture the natural movements of ocean currents and the flow of swells to generate power.

How to Calculate Group Velocity of Waves?

Group Velocity of Waves calculator 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 calculate the Group Velocity of Waves, The Group Velocity of Waves 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 calculate Group Velocity of Waves using this online calculator? To use this online calculator for Group Velocity of Waves, enter Wave Speed (v), Wave Number for Water Wave (k) & Coastal Mean Depth (d) and hit the calculate button. Here is how the Group Velocity of Waves calculation can be explained with given input values -> 28.66436 = 0.5*50*(1+((0.2*10)/(sinh(0.2*10)*cosh(0.2*10)))).

FAQ

What is Group Velocity of Waves?

The Group Velocity of Waves 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 and is represented as V_g = 0.5*v*(1+((k*d)/(sinh(k*d)*cosh(k*d)))) or 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)))). Wave Speed is the rate at which a wave travels through a medium, measured in distance per unit time, Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance & Coastal Mean Depth refers to the average depth of water over a particular area, such as a section of coastline, a bay, or an ocean basin.

How to calculate Group Velocity of Waves?

The Group Velocity of Waves 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 is calculated using 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 calculate Group Velocity of Waves, you need Wave Speed (v), Wave Number for Water Wave (k) & Coastal Mean Depth (d). With our tool, you need to enter the respective value for Wave Speed, Wave Number for Water Wave & Coastal Mean Depth 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 Group Velocity of Waves?

In this formula, Group Velocity of Waves uses Wave Speed, Wave Number for Water Wave & Coastal Mean Depth. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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