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Wave Speed given Group Velocity Formula

GoWave Speed Formula

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Wave Speed is the rate at which a wave travels through a medium, measured in distance per unit time. Check FAQs

v = \frac{V g}{0.5 \cdot (1 + (\frac{k \cdot d}{\sinh (k \cdot d) \cdot \cosh (k \cdot d)}))}

v - Wave Speed?V_g - Group Velocity of Waves?k - Wave Number for Water Wave?d - Coastal Mean Depth?

Wave Speed given Group Velocity Example

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Here is how the Wave Speed given Group Velocity equation looks like with Values.

Here is how the Wave Speed given Group Velocity equation looks like with Units.

Here is how the Wave Speed given Group Velocity equation looks like.

49.9924 = \frac{28.66}{0.5 \cdot (1 + (\frac{0.2 \cdot 10}{\sinh (0.2 \cdot 10) \cdot \cosh (0.2 \cdot 10)}))}

49.9924m/s = \frac{28.66m/s}{0.5 \cdot (1 + (\frac{0.2 \cdot 10m}{\sinh (0.2 \cdot 10m) \cdot \cosh (0.2 \cdot 10m)}))}

49.9924 = \frac{28.66}{0.5 \cdot (1 + (\frac{0.2 \cdot 10}{\sinh (0.2 \cdot 10) \cdot \cosh (0.2 \cdot 10)}))}

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Wave Speed given Group Velocity Solution

Follow our step by step solution on how to calculate Wave Speed given Group Velocity?

FIRST Step Consider the formula

v = \frac{V g}{0.5 \cdot (1 + (\frac{k \cdot d}{\sinh (k \cdot d) \cdot \cosh (k \cdot d)}))}

Next Step Substitute values of Variables

∴

v = \frac{28.66m/s}{0.5 \cdot (1 + (\frac{0.2 \cdot 10m}{\sinh (0.2 \cdot 10m) \cdot \cosh (0.2 \cdot 10m)}))}

Next Step Prepare to Evaluate

∴

v = \frac{28.66}{0.5 \cdot (1 + (\frac{0.2 \cdot 10}{\sinh (0.2 \cdot 10) \cdot \cosh (0.2 \cdot 10)}))}

Next Step Evaluate

∴

v = 49.9923999122297m/s

LAST Step Rounding Answer

∴

v = 49.9924m/s

Wave Speed given Group Velocity Formula Elements

Variables

Functions

Wave Speed

Wave Speed is the rate at which a wave travels through a medium, measured in distance per unit time.

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Wave Speed

Group Velocity of Waves

The Group Velocity of Waves refers to the velocity at which the overall shape or envelope of a wave group propagates through a medium.

Symbol: V_g

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Group Velocity of Waves

Wave Number for Water Wave

Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wave Number for Water Wave

Coastal Mean Depth

Coastal Mean Depth of a fluid flow is a measure of the average depth of the fluid in a channel, pipe, or other conduit through which the fluid is flowing.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Coastal Mean Depth

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)

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.

Syntax: cosh(Number)

Other Formulas to find Wave Speed

Go Wave Speed

v = \frac{ω}{k''}

Other formulas in Group Velocity, Beats, Energy Transport category

Go Wave Power per unit Crest Width

P = E \cdot V g

Go Total Energy per unit Area given Wave Power per unit Crest Width

E = \frac{P}{V g}

Go Group Velocity given Wave Power per unit Crest Width

V g = \frac{P}{E}

Go Radian Frequency given Wave Propagation

ω = k \cdot x

How to Evaluate Wave Speed given Group Velocity?

Wave Speed given Group Velocity evaluator uses Wave Speed = Group Velocity of Waves/(0.5*(1+((Wave Number for Water Wave*Coastal Mean Depth)/(sinh(Wave Number for Water Wave*Coastal Mean Depth)*cosh(Wave Number for Water Wave*Coastal Mean Depth))))) to evaluate the Wave Speed, The Wave Speed given Group Velocity is defined as how fast wave travels and is determined by properties of medium in which wave is moving and when the group velocity is given. Wave Speed is denoted by v symbol.

How to evaluate Wave Speed given Group Velocity using this online evaluator? To use this online evaluator for Wave Speed given Group Velocity, enter Group Velocity of Waves (V_g), Wave Number for Water Wave (k) & Coastal Mean Depth (d) and hit the calculate button.

FAQs on Wave Speed given Group Velocity

What is the formula to find Wave Speed given Group Velocity?

The formula of Wave Speed given Group Velocity is expressed as Wave Speed = Group Velocity of Waves/(0.5*(1+((Wave Number for Water Wave*Coastal Mean Depth)/(sinh(Wave Number for Water Wave*Coastal Mean Depth)*cosh(Wave Number for Water Wave*Coastal Mean Depth))))). Here is an example- 49.9924 = 28.66/(0.5*(1+((0.2*10)/(sinh(0.2*10)*cosh(0.2*10))))).

How to calculate Wave Speed given Group Velocity?

With Group Velocity of Waves (V_g), Wave Number for Water Wave (k) & Coastal Mean Depth (d) we can find Wave Speed given Group Velocity using the formula - Wave Speed = Group Velocity of Waves/(0.5*(1+((Wave Number for Water Wave*Coastal Mean Depth)/(sinh(Wave Number for Water Wave*Coastal Mean Depth)*cosh(Wave Number for Water Wave*Coastal Mean Depth))))). This formula also uses Hyperbolic Sine (sinh), Hyperbolic Cosine (cosh) function(s).

What are the other ways to Calculate Wave Speed?

Here are the different ways to Calculate Wave Speed-

Wave Speed=Wave Angular Frequency/Wave Number

Can the Wave Speed given Group Velocity be negative?

Yes, the Wave Speed given Group Velocity, measured in Speed can be negative.

Which unit is used to measure Wave Speed given Group Velocity?

Wave Speed given Group Velocity 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 Wave Speed given Group Velocity can be measured.

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