Group Velocity of Wave given Wavelength and Wave Period Calculator

✖Wavelength is the distance between successive peaks or troughs of a wave. It is crucial in understanding the behavior of waves, particularly in relation to subsurface pressure.ⓘ Wavelength [λ]			+10% -10%
✖Wave Period is the time it takes for one complete wave cycle to pass a fixed point. It affects wave energy, with longer periods indicating more energy and potential for erosion.ⓘ Wave Period [P]			+10% -10%
✖Water Depth is vertical distance from the surface of a body of water to its bottom, it is a critical parameter for understanding the characteristics and behaviors of the marine environment.ⓘ Water Depth [d]			+10% -10%

✖Group Velocity for Shallow Water is the speed at which a group of waves travels through shallow water, crucial for understanding how energy and momentum are transferred within wave groups.ⓘ Group Velocity of Wave given Wavelength and Wave Period [Vg_shallow]

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Group Velocity of Wave given Wavelength and Wave Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Group Velocity for Shallow Water = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength)))
Vg_shallow = 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 for Shallow Water - (Measured in Meter per Second) - Group Velocity for Shallow Water is the speed at which a group of waves travels through shallow water, crucial for understanding how energy and momentum are transferred within wave groups.
Wavelength - (Measured in Meter) - Wavelength is the distance between successive peaks or troughs of a wave. It is crucial in understanding the behavior of waves, particularly in relation to subsurface pressure.
Wave Period - Wave Period is the time it takes for one complete wave cycle to pass a fixed point. It affects wave energy, with longer periods indicating more energy and potential for erosion.
Water Depth - (Measured in Meter) - Water Depth is vertical distance from the surface of a body of water to its bottom, it is a critical parameter for understanding the characteristics and behaviors of the marine environment.

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_shallow = 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_shallow = 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 for Shallow Water

(Calculation completed in 00.004 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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< Group Velocity Calculators

Group Velocity of Wave given Wavelength and Wave Period

LaTeX Go Group Velocity for Shallow Water = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength)))

Group Velocity for Deepwater

LaTeX Go Group Velocity for Deep Water = 0.5*(Deep Water Wavelength/Surf Zone Wave Period)

Deepwater Wavelength

LaTeX Go Deep Water Wavelength = (Group Velocity for Deep Water*Wave Period)/0.5

Deepwater Celerity

LaTeX Go Deep Water Wave Celerity = Group Velocity for Deep Water/0.5

Group Velocity of Wave given Wavelength and Wave Period Formula

LaTeX Go

Group Velocity for Shallow Water = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength)))
Vg_shallow = 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 for Shallow Water = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength))) to calculate the Group Velocity for Shallow Water, The Group Velocity of Wave given Wavelength and Wave Period Formula is defined as the speed at which the wave energy propagates through shallow water, such as near the coast or in a shallow basin. It is determined by combining the wave's wavelength and wave period. Group Velocity for Shallow Water is denoted by Vg_shallow 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 -> 25.50832 = 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?

The Group Velocity of Wave given Wavelength and Wave Period Formula is defined as the speed at which the wave energy propagates through shallow water, such as near the coast or in a shallow basin. It is determined by combining the wave's wavelength and wave period and is represented as Vg_shallow = 0.5*(λ/P)*(1+(4*pi*d/λ)/(sinh(4*pi*d/λ))) or Group Velocity for Shallow Water = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength))). Wavelength is the distance between successive peaks or troughs of a wave. It is crucial in understanding the behavior of waves, particularly in relation to subsurface pressure, Wave Period is the time it takes for one complete wave cycle to pass a fixed point. It affects wave energy, with longer periods indicating more energy and potential for erosion & Water Depth is vertical distance from the surface of a body of water to its bottom, it is a critical parameter for understanding the characteristics and behaviors of the marine environment.

How to calculate Group Velocity of Wave given Wavelength and Wave Period?

The Group Velocity of Wave given Wavelength and Wave Period Formula is defined as the speed at which the wave energy propagates through shallow water, such as near the coast or in a shallow basin. It is determined by combining the wave's wavelength and wave period is calculated using Group Velocity for Shallow Water = 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 for Shallow Water?

In this formula, Group Velocity for Shallow Water uses Wavelength, Wave Period & Water Depth. We can use 1 other way(s) to calculate the same, which is/are as follows -

Group Velocity for Shallow Water = Wavelength/Wave Period

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