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*Mean Depth)/(sinh(Wave Number for Water Wave*Mean Depth)*cosh(Wave Number for Water Wave*Mean Depth)))))
v = Vg/(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 is the velocity with which the overall envelope shape of the wave's amplitudes; known as the modulation.
Wave Number for Water Wave - The wave number for water waves quantifies the number of waves per unit length along the surface of the water.
Mean Depth - (Measured in Meter) - Mean Depth for Steady two-dimensional waves.
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
Mean Depth: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
v = Vg/(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 00.004 seconds)

Credits

Created by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
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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*Mean Depth)/(sinh(Wave Number for Water Wave*Mean Depth)*cosh(Wave Number for Water Wave*Mean Depth)))))
Group Velocity of Waves
Go Group Velocity of Waves = 0.5*Wave Speed*(1+((Wave Number for Water Wave*Mean Depth)/(sinh(Wave Number for Water Wave*Mean Depth)*cosh(Wave Number for Water Wave*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 of 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 of Area
Wave Power per unit Crest Width
Go Wave Power per unit Crest Width = Total Energy per unit of Area*Group Velocity of Waves
Wavenumber given Wave Speed
Go Wave Number for Water Wave = Wave Angular Frequency/Wave Speed
Wave Speed
Go Wave Speed = Wave Angular Frequency/Wave Number for Water Wave

Wave Speed given Group Velocity Formula

Wave Speed = Group Velocity of Waves/(0.5*(1+((Wave Number for Water Wave*Mean Depth)/(sinh(Wave Number for Water Wave*Mean Depth)*cosh(Wave Number for Water Wave*Mean Depth)))))
v = Vg/(0.5*(1+((k*d)/(sinh(k*d)*cosh(k*d)))))

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*Mean Depth)/(sinh(Wave Number for Water Wave*Mean Depth)*cosh(Wave Number for Water Wave*Mean Depth))))) to calculate the Wave Speed, Wave Speed given Group Velocity is how fast wave travels and is determined by properties of medium in which wave is moving. 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 (Vg), Wave Number for Water Wave (k) & 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 -> 1.8141 = 28.66/(0.5*(1+((0.2*10)/(sinh(0.2*10)*cosh(0.2*10))))).

FAQ

What is Wave Speed given Group Velocity?
Wave Speed given Group Velocity is how fast wave travels and is determined by properties of medium in which wave is moving and is represented as v = Vg/(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*Mean Depth)/(sinh(Wave Number for Water Wave*Mean Depth)*cosh(Wave Number for Water Wave*Mean Depth))))). The Group Velocity of Waves is the velocity with which the overall envelope shape of the wave's amplitudes; known as the modulation, The wave number for water waves quantifies the number of waves per unit length along the surface of the water & Mean Depth for Steady two-dimensional waves.
How to calculate Wave Speed given Group Velocity?
Wave Speed given Group Velocity is how fast wave travels and is determined by properties of medium in which wave is moving is calculated using Wave Speed = Group Velocity of Waves/(0.5*(1+((Wave Number for Water Wave*Mean Depth)/(sinh(Wave Number for Water Wave*Mean Depth)*cosh(Wave Number for Water Wave*Mean Depth))))). To calculate Wave Speed given Group Velocity, you need Group Velocity of Waves (Vg), Wave Number for Water Wave (k) & Mean Depth (d). With our tool, you need to enter the respective value for Group Velocity of Waves, Wave Number for Water Wave & 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 & 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 for Water Wave
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