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Group Velocity of Wave given Wavelength and Wave Period Formula

GoGroup Velocity for Shallow Water Formula

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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. Check FAQs

Vg shallow = 0.5 \cdot (\frac{λ}{P}) \cdot (1 + \frac{4 \cdot π \cdot \frac{d}{λ}}{\sinh (4 \cdot π \cdot \frac{d}{λ})})

Vg_shallow - Group Velocity for Shallow Water?λ - Wavelength?P - Wave Period?d - Water Depth?π - Archimedes' constant?

Group Velocity of Wave given Wavelength and Wave Period Example

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Here is how the Group Velocity of Wave given Wavelength and Wave Period equation looks like with Values.

Here is how the Group Velocity of Wave given Wavelength and Wave Period equation looks like with Units.

Here is how the Group Velocity of Wave given Wavelength and Wave Period equation looks like.

25.5083 = 0.5 \cdot (\frac{26.8}{1.03}) \cdot (1 + \frac{4 \cdot 3.1416 \cdot \frac{1.05}{26.8}}{\sinh (4 \cdot 3.1416 \cdot \frac{1.05}{26.8})})

25.5083m/s = 0.5 \cdot (\frac{26.8m}{1.03}) \cdot (1 + \frac{4 \cdot 3.1416 \cdot \frac{1.05m}{26.8m}}{\sinh (4 \cdot 3.1416 \cdot \frac{1.05m}{26.8m})})

25.5083 = 0.5 \cdot (\frac{26.8}{1.03}) \cdot (1 + \frac{4 \cdot 3.1416 \cdot \frac{1.05}{26.8}}{\sinh (4 \cdot 3.1416 \cdot \frac{1.05}{26.8})})

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Group Velocity of Wave given Wavelength and Wave Period Solution

Follow our step by step solution on how to calculate Group Velocity of Wave given Wavelength and Wave Period?

FIRST Step Consider the formula

Vg shallow = 0.5 \cdot (\frac{λ}{P}) \cdot (1 + \frac{4 \cdot π \cdot \frac{d}{λ}}{\sinh (4 \cdot π \cdot \frac{d}{λ})})

Next Step Substitute values of Variables

∴

Vg shallow = 0.5 \cdot (\frac{26.8m}{1.03}) \cdot (1 + \frac{4 \cdot π \cdot \frac{1.05m}{26.8m}}{\sinh (4 \cdot π \cdot \frac{1.05m}{26.8m})})

Next Step Substitute values of Constants

∴

Vg shallow = 0.5 \cdot (\frac{26.8m}{1.03}) \cdot (1 + \frac{4 \cdot 3.1416 \cdot \frac{1.05m}{26.8m}}{\sinh (4 \cdot 3.1416 \cdot \frac{1.05m}{26.8m})})

Next Step Prepare to Evaluate

∴

Vg shallow = 0.5 \cdot (\frac{26.8}{1.03}) \cdot (1 + \frac{4 \cdot 3.1416 \cdot \frac{1.05}{26.8}}{\sinh (4 \cdot 3.1416 \cdot \frac{1.05}{26.8})})

Next Step Evaluate

∴

Vg shallow = 25.5083227276637m/s

LAST Step Rounding Answer

∴

Vg shallow = 25.5083m/s

Group Velocity of Wave given Wavelength and Wave Period Formula Elements

Variables

Constants

Functions

Group Velocity for Shallow Water

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.

Symbol: Vg_shallow

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Group Velocity for Shallow Water

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.

Symbol: λ

Measurement: WavelengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wavelength

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.

Symbol: P

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wave Period

Water Depth

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.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Water Depth

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sinh(Number)

Other Formulas to find Group Velocity for Shallow Water

Go Group Velocity for Shallow Water

Vg shallow = \frac{λ}{P}

Other formulas in Group Velocity category

Go Group Velocity for Deepwater

Vg deep = 0.5 \cdot (\frac{λ o}{P sz})

Go Deepwater Wavelength

λ o = \frac{Vg deep \cdot P}{0.5}

Go Deepwater Celerity

C o = \frac{Vg deep}{0.5}

Go Group Velocity given Deepwater Celerity

Vg deep = 0.5 \cdot C o

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

Group Velocity of Wave given Wavelength and Wave Period evaluator uses Group Velocity for Shallow Water = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength))) to evaluate 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 evaluate Group Velocity of Wave given Wavelength and Wave Period using this online evaluator? To use this online evaluator for Group Velocity of Wave given Wavelength and Wave Period, enter Wavelength (λ), Wave Period (P) & Water Depth (d) and hit the calculate button.

FAQs on Group Velocity of Wave given Wavelength and Wave Period

What is the formula to find Group Velocity of Wave given Wavelength and Wave Period?

The formula of Group Velocity of Wave given Wavelength and Wave Period is expressed as Group Velocity for Shallow Water = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength))). Here is an example- 25.50832 = 0.5*(26.8/1.03)*(1+(4*pi*1.05/26.8)/(sinh(4*pi*1.05/26.8))).

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

With Wavelength (λ), Wave Period (P) & Water Depth (d) we can find Group Velocity of Wave given Wavelength and Wave Period using the formula - Group Velocity for Shallow Water = 0.5*(Wavelength/Wave Period)*(1+(4*pi*Water Depth/Wavelength)/(sinh(4*pi*Water Depth/Wavelength))). This formula also uses Archimedes' constant and Hyperbolic Sine (sinh) function(s).

What are the other ways to Calculate Group Velocity for Shallow Water?

Here are the different ways to Calculate Group Velocity for Shallow Water-

Group Velocity for Shallow Water=Wavelength/Wave Period

Can the Group Velocity of Wave given Wavelength and Wave Period be negative?

Yes, the Group Velocity of Wave given Wavelength and Wave Period, measured in Speed can be negative.

Which unit is used to measure Group Velocity of Wave given Wavelength and Wave Period?

Group Velocity of Wave given Wavelength and Wave Period is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Group Velocity of Wave given Wavelength and Wave Period can be measured.

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Group Velocity of Wave given Wavelength and Wave Period Formula

​GoGroup Velocity for Shallow Water Formula

Group Velocity of Wave given Wavelength and Wave Period Example

Group Velocity of Wave given Wavelength and Wave Period Solution

Group Velocity of Wave given Wavelength and Wave Period Formula Elements

Other Formulas to find Group Velocity for Shallow Water

Other formulas in Group Velocity category

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

FAQs on Group Velocity of Wave given Wavelength and Wave Period

Variable Name

GoGroup Velocity for Shallow Water Formula