Group velocity of Wave given Wavelength and Wave Period Solution

STEP 0: Pre-Calculation Summary
Formula Used
Group Velocity = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength)))
Vg = 0.5*(λ/P)*(1+(4*pi*d/λ)/(sinh(4*pi*d/λ)))
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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)
Variables Used
Group Velocity - (Measured in Meter per Second) - Group Velocity is the velocity with which the overall envelope shape of the wave's amplitudes; known as the modulation.
Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Wave Period - Wave Period is the time between successive peaks or troughs.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body.
STEP 1: Convert Input(s) to Base Unit
Wavelength: 26.8 Meter --> 26.8 Meter No Conversion Required
Wave Period: 1.03 --> No Conversion Required
Water Depth: 1.05 Meter --> 1.05 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Vg = 0.5*(λ/P)*(1+(4*pi*d/λ)/(sinh(4*pi*d/λ))) --> 0.5*(26.8/1.03)*(1+(4*pi*1.05/26.8)/(sinh(4*pi*1.05/26.8)))
Evaluating ... ...
Vg = 25.5083227276637
STEP 3: Convert Result to Output's Unit
25.5083227276637 Meter per Second --> No Conversion Required
FINAL ANSWER
25.5083227276637 25.50832 Meter per Second <-- Group Velocity
(Calculation completed in 00.004 seconds)

Credits

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Coorg Institute of Technology (CIT), Coorg
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NSS College of Engineering (NSSCE), Palakkad
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8 Group Velocity Calculators

Group velocity of Wave given Wavelength and Wave Period
Go Group Velocity = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength)))
Group Velocity for Deepwater
Go Group Velocity = 0.5*(Deep-Water Wavelength/Surf Zone Wave period)
Deepwater Wavelength
Go Deep-Water Wavelength = (Group Velocity*Wave Period)/0.5
Wave Period given Group Velocity for Shallow Water
Go Surf Zone Wave period = Wavelength/Group Velocity
Wavelength given Group Velocity of Shallow Water
Go Wavelength = Group Velocity*Annual Wave Period
Group Velocity for Shallow Water
Go Group Velocity = Wavelength/Wave Period
Group Velocity given Deepwater Celerity
Go Group Velocity = 0.5*Deepwater Wave Celerity
Deepwater Celerity
Go Deepwater Wave Celerity = Group Velocity/0.5

Group velocity of Wave given Wavelength and Wave Period Formula

Group Velocity = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength)))
Vg = 0.5*(λ/P)*(1+(4*pi*d/λ)/(sinh(4*pi*d/λ)))

What is Wavelength?

Wavelength, distance between corresponding points of two consecutive waves. “Corresponding points” refers to two points or particles in the same phase i.e., points that have completed identical fractions of their periodic motion.

How to Calculate Group velocity of Wave given Wavelength and Wave Period?

Group velocity of Wave given Wavelength and Wave Period calculator uses Group Velocity = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength))) to calculate the Group Velocity, Group velocity of Wave given Wavelength and Wave Period is 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 is denoted by Vg symbol.

How to calculate Group velocity of Wave given Wavelength and Wave Period using this online calculator? To use this online calculator for Group velocity of Wave given Wavelength and Wave Period, enter Wavelength (λ), Wave Period (P) & Water Depth (d) and hit the calculate button. Here is how the Group velocity of Wave given Wavelength and Wave Period calculation can be explained with given input values -> 25.55465 = 0.5*(26.8/1.03)*(1+(4*pi*1.05/26.8)/(sinh(4*pi*1.05/26.8))).

FAQ

What is Group velocity of Wave given Wavelength and Wave Period?
Group velocity of Wave given Wavelength and Wave Period is 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 Vg = 0.5*(λ/P)*(1+(4*pi*d/λ)/(sinh(4*pi*d/λ))) or Group Velocity = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength))). Wavelength can be defined as the distance between two successive crests or troughs of a wave, Wave Period is the time between successive peaks or troughs & Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body.
How to calculate Group velocity of Wave given Wavelength and Wave Period?
Group velocity of Wave given Wavelength and Wave Period is 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 = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength))). To calculate Group velocity of Wave given Wavelength and Wave Period, you need Wavelength (λ), Wave Period (P) & Water Depth (d). With our tool, you need to enter the respective value for Wavelength, Wave Period & Water 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?
In this formula, Group Velocity uses Wavelength, Wave Period & Water Depth. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Group Velocity = 0.5*(Deep-Water Wavelength/Surf Zone Wave period)
  • Group Velocity = 0.5*Deepwater Wave Celerity
  • Group Velocity = Wavelength/Wave Period
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