Wave Speed given Group Velocity Calculator

✖The Group Velocity of Waves refers to the velocity at which the overall shape or envelope of a wave group propagates through a medium.ⓘ Group Velocity of Waves [V_g]			+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 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.ⓘ Coastal Mean Depth [d]			+10% -10%

✖Wave Speed is the rate at which a wave travels through a medium, measured in distance per unit time.ⓘ Wave Speed given Group Velocity [v]

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Wave Speed given Group Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))))
v = V_g/(0.5*(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

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.
Group Velocity of Waves - (Measured in Meter per Second) - The Group Velocity of Waves refers to the velocity at which the overall shape or envelope of a wave group propagates through a medium.
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 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.

STEP 1: Convert Input(s) to Base Unit

Group Velocity of Waves: 28.66 Meter per Second --> 28.66 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 = V_g/(0.5*(1+((k*d)/(sinh(k*d)*cosh(k*d))))) --> 28.66/(0.5*(1+((0.2*10)/(sinh(0.2*10)*cosh(0.2*10)))))

Evaluating ... ...

v = 49.9923999122297

STEP 3: Convert Result to Output's Unit

49.9923999122297 Meter per Second --> No Conversion Required

FINAL ANSWER

49.9923999122297 ≈ 49.9924 Meter per Second <-- Wave Speed

(Calculation completed in 00.005 seconds)

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Credits

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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< Group Velocity, Beats, Energy Transport Calculators

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Group Velocity given Wave Power per unit Crest Width

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

Wave Power per unit Crest Width

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

Wave Speed

LaTeX Go Wave Speed = Wave Angular Frequency/Wave Number

Wave Speed given Group Velocity Formula

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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 Wave Speed given Group Velocity?

Wave Speed given Group Velocity calculator uses 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))))) to calculate the Wave Speed, The Wave Speed given Group Velocity is defined as how fast wave travels and is determined by properties of medium in which wave is moving and when the group velocity is given. Wave Speed is denoted by v symbol.

How to calculate Wave Speed given Group Velocity using this online calculator? To use this online calculator for Wave Speed given Group Velocity, enter Group Velocity of Waves (V_g), Wave Number for Water Wave (k) & Coastal Mean Depth (d) and hit the calculate button. Here is how the Wave Speed given Group Velocity calculation can be explained with given input values -> 49.9924 = 28.66/(0.5*(1+((0.2*10)/(sinh(0.2*10)*cosh(0.2*10))))).

FAQ

What is Wave Speed given Group Velocity?

The Wave Speed given Group Velocity is defined as how fast wave travels and is determined by properties of medium in which wave is moving and when the group velocity is given and is represented as v = V_g/(0.5*(1+((k*d)/(sinh(k*d)*cosh(k*d))))) or 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))))). The Group Velocity of Waves refers to the velocity at which the overall shape or envelope of a wave group propagates through a medium, Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance & 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.

How to calculate Wave Speed given Group Velocity?

The Wave Speed given Group Velocity is defined as how fast wave travels and is determined by properties of medium in which wave is moving and when the group velocity is given is calculated using 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))))). To calculate Wave Speed given Group Velocity, you need Group Velocity of Waves (V_g), Wave Number for Water Wave (k) & Coastal Mean Depth (d). With our tool, you need to enter the respective value for Group Velocity of Waves, 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 Wave Speed?

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

Wave Speed = Wave Angular Frequency/Wave Number

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