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Ratio of Wave Group Speed and Phase Speed Formula

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Ratio of Wave Group Speed and Phase Speed is ratio of the group speed (cg) the speed with which the energy of the waves moves, while the phase speed (c) the velocity of a wave crest. Check FAQs

n = \frac{S xy \cdot 8}{ρ \cdot [g] \cdot H^{2} \cdot \cos (α) \cdot \sin (α)}

n - Ratio of Wave Group Speed and Phase Speed?S_xy - Radiation Stress Component?ρ - Mass Density?H - Wave Height?α - Wave Crest Angle?[g] - Gravitational acceleration on Earth?

Ratio of Wave Group Speed and Phase Speed Example

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Here is how the Ratio of Wave Group Speed and Phase Speed equation looks like with Values.

Here is how the Ratio of Wave Group Speed and Phase Speed equation looks like with Units.

Here is how the Ratio of Wave Group Speed and Phase Speed equation looks like.

0.0556 = \frac{15 \cdot 8}{997 \cdot 9.8066 \cdot {0.714}^{2} \cdot \cos (60) \cdot \sin (60)}

0.0556 = \frac{15 \cdot 8}{997kg/m³ \cdot 9.8066m/s² \cdot {0.714m}^{2} \cdot \cos (60°) \cdot \sin (60°)}

0.0556 = \frac{15 \cdot 8}{997 \cdot 9.8066 \cdot {0.714}^{2} \cdot \cos (60) \cdot \sin (60)}

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Ratio of Wave Group Speed and Phase Speed Solution

Follow our step by step solution on how to calculate Ratio of Wave Group Speed and Phase Speed?

FIRST Step Consider the formula

n = \frac{S xy \cdot 8}{ρ \cdot [g] \cdot H^{2} \cdot \cos (α) \cdot \sin (α)}

Next Step Substitute values of Variables

∴

n = \frac{15 \cdot 8}{997kg/m³ \cdot [g] \cdot {0.714m}^{2} \cdot \cos (60°) \cdot \sin (60°)}

Next Step Substitute values of Constants

∴

n = \frac{15 \cdot 8}{997kg/m³ \cdot 9.8066m/s² \cdot {0.714m}^{2} \cdot \cos (60°) \cdot \sin (60°)}

Next Step Convert Units

∴

n = \frac{15 \cdot 8}{997kg/m³ \cdot 9.8066m/s² \cdot {0.714m}^{2} \cdot \cos (1.0472rad) \cdot \sin (1.0472rad)}

Next Step Prepare to Evaluate

∴

n = \frac{15 \cdot 8}{997 \cdot 9.8066 \cdot {0.714}^{2} \cdot \cos (1.0472) \cdot \sin (1.0472)}

Next Step Evaluate

∴

n = 0.0555991756603236

LAST Step Rounding Answer

∴

n = 0.0556

Ratio of Wave Group Speed and Phase Speed Formula Elements

Variables

Constants

Functions

Ratio of Wave Group Speed and Phase Speed

Ratio of Wave Group Speed and Phase Speed is ratio of the group speed (cg) the speed with which the energy of the waves moves, while the phase speed (c) the velocity of a wave crest.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Ratio of Wave Group Speed and Phase Speed

Radiation Stress Component

Radiation Stress Component is the momentum transferred through the water body per unit of time (the flux of momentum) by wave orbital motion.

Symbol: S_xy

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Radiation Stress Component

Mass Density

Mass Density is a physical quantity that represents the mass of a substance per unit volume.

Symbol: ρ

Measurement: Mass ConcentrationUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Mass Density

Wave Height

Wave Height of a surface wave is the difference between the elevations of a crest and a neighbouring trough.

Symbol: H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Wave Height

Wave Crest Angle

Wave Crest Angle is the angle at which the crest of a wave approaches or intersects with another medium, such as the shoreline or another wave.

Symbol: α

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Wave Crest Angle

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Longshore Current category

Go Radiation Stress Component

S xy = (\frac{n}{8}) \cdot ρ \cdot [g] \cdot (H^{2}) \cdot \cos (α) \cdot \sin (α)

Go Wave Height given Radiation Stress Component

H = \sqrt{\frac{S xy \cdot 8}{ρ} \cdot [g] \cdot \cos (α) \cdot \sin (α)}

Go Longshore Current Speed

V = (5 \cdot \frac{π}{16}) \cdot \tan (β *) \cdot γ b \cdot \sqrt{[g] \cdot D} \cdot \sin (α) \cdot \frac{\cos (α)}{C f}

Go Beach Slope Modified for Wave Setup

β * = a \tan (\frac{\tan (β)}{1 + (3 \cdot \frac{{γ b}^{2}}{8})})

How to Evaluate Ratio of Wave Group Speed and Phase Speed?

Ratio of Wave Group Speed and Phase Speed evaluator uses Ratio of Wave Group Speed and Phase Speed = (Radiation Stress Component*8)/(Mass Density*[g]*Wave Height^2*cos(Wave Crest Angle)*sin(Wave Crest Angle)) to evaluate the Ratio of Wave Group Speed and Phase Speed, The Ratio of Wave Group Speed and Phase Speed is defined as the ratio of the speed at which a wave packet, or group of waves, travels to the speed at which the phase of a wave travels. Ratio of Wave Group Speed and Phase Speed is denoted by n symbol.

How to evaluate Ratio of Wave Group Speed and Phase Speed using this online evaluator? To use this online evaluator for Ratio of Wave Group Speed and Phase Speed, enter Radiation Stress Component (S_xy), Mass Density (ρ), Wave Height (H) & Wave Crest Angle (α) and hit the calculate button.

FAQs on Ratio of Wave Group Speed and Phase Speed

What is the formula to find Ratio of Wave Group Speed and Phase Speed?

The formula of Ratio of Wave Group Speed and Phase Speed is expressed as Ratio of Wave Group Speed and Phase Speed = (Radiation Stress Component*8)/(Mass Density*[g]*Wave Height^2*cos(Wave Crest Angle)*sin(Wave Crest Angle)). Here is an example- 0.055599 = (15*8)/(997*[g]*0.714^2*cos(1.0471975511964)*sin(1.0471975511964)).

How to calculate Ratio of Wave Group Speed and Phase Speed?

With Radiation Stress Component (S_xy), Mass Density (ρ), Wave Height (H) & Wave Crest Angle (α) we can find Ratio of Wave Group Speed and Phase Speed using the formula - Ratio of Wave Group Speed and Phase Speed = (Radiation Stress Component*8)/(Mass Density*[g]*Wave Height^2*cos(Wave Crest Angle)*sin(Wave Crest Angle)). This formula also uses Gravitational acceleration on Earth constant(s) and , Sine (sin), Cosine (cos) function(s).

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Ratio of Wave Group Speed and Phase Speed Formula

Ratio of Wave Group Speed and Phase Speed Example

Ratio of Wave Group Speed and Phase Speed Solution

Ratio of Wave Group Speed and Phase Speed Formula Elements

Other formulas in Longshore Current category

How to Evaluate Ratio of Wave Group Speed and Phase Speed?

FAQs on Ratio of Wave Group Speed and Phase Speed

Variable Name