Dimensionless Wave Speed Calculator

✖Propagation Velocity refers to the speed at which waves or other disturbances propagate through water.ⓘ Propagation Velocity [v_p']			+10% -10%
✖Coastal Mean Depth is the average water depth over a particular area, such as a section of coastline, a bay, or an ocean basin.ⓘ Coastal Mean Depth [d]			+10% -10%

✖Wave Speed is the rate at which a wave travels through a medium, measured in distance per unit time.ⓘ Dimensionless Wave Speed [v]

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Formula

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Dimensionless Wave Speed

Formula

`"v" = "v"_{"p'"}/sqrt("[g]"*"d")`

Example

`"50.00579m/s"="495.2m/s"/sqrt("[g]"*"10m")`

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Dimensionless Wave Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wave Speed = Propagation Velocity/sqrt([g]*Coastal Mean Depth)
v = v_p'/sqrt([g]*d)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Wave Speed - (Measured in Meter per Second) - Wave Speed is the rate at which a wave travels through a medium, measured in distance per unit time.
Propagation Velocity - (Measured in Meter per Second) - Propagation Velocity refers to the speed at which waves or other disturbances propagate through water.
Coastal Mean Depth - (Measured in Meter) - Coastal Mean Depth is the average water depth over a particular area, such as a section of coastline, a bay, or an ocean basin.

STEP 1: Convert Input(s) to Base Unit

Propagation Velocity: 495.2 Meter per Second --> 495.2 Meter per Second No Conversion Required
Coastal Mean Depth: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v = v_p'/sqrt([g]*d) --> 495.2/sqrt([g]*10)

Evaluating ... ...

v = 50.0057906330592

STEP 3: Convert Result to Output's Unit

50.0057906330592 Meter per Second --> No Conversion Required

FINAL ANSWER

50.0057906330592 ≈ 50.00579 Meter per Second <-- Wave Speed

(Calculation completed in 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< 12 Linear Dispersion Relation of Linear Wave Calculators

Velocity of Propagation in Linear Dispersion Relation given Wavelength

Go Velocity of Propagation = sqrt(([g]*Coastal Mean Depth*tanh(2*pi*Coastal Mean Depth/Deep Water Wavelength of Coast))/(2*pi*Coastal Mean Depth/Deep Water Wavelength of Coast))

Guo Formula of Linear Dispersion Relation for Wave Number

Go Wave Number for Water Wave = ((Angular Frequency of Wave^2*Coastal Mean Depth)/[g])*(1-exp(-(Angular Frequency of Wave*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5)))/Coastal Mean Depth

Guo Formula of Linear Dispersion Relation

Go Linear Dispersion Relation = (Wave Angular Frequency^2*Coastal Mean Depth/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Coastal Mean Depth/[g])^(5/2))^(-2/5)))

Velocity of Propagation in Linear Dispersion Relation

Go Velocity of Propagation = sqrt(([g]*Coastal Mean Depth*tanh(Wave Number for Water Wave*Coastal Mean Depth))/(Wave Number for Water Wave*Coastal Mean Depth))

Wave Number of Convenient Empirical Explicit Approximation

Go Wave Number for Water Wave = (Angular Frequency of Wave^2/[g])*(coth((Angular Frequency of Wave*sqrt(Coastal Mean Depth/[g])^(3/2))^(2/3)))

Radian Frequency of Wave

Go Angular Frequency of Wave = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Coastal Mean Depth))

Dimensionless Wave Speed

Go Wave Speed = Propagation Velocity/sqrt([g]*Coastal Mean Depth)

Wave Number for Steady Two-dimensional Waves

Go Wave Number for Water Wave = (2*pi)/Deep Water Wavelength of Coast

Wavelength given Wave Number

Go Deep Water Wavelength of Coast = (2*pi)/Wave Number for Water Wave

Relative Wavelength

Go Relative Wavelength = Deep-Water Wavelength/Coastal Mean Depth

Wave period given Radian Frequency of Waves

Go Wave Period = 2*pi/Wave Angular Frequency

Radian Frequency of Waves

Go Wave Angular Frequency = 2*pi/Wave Period

Dimensionless Wave Speed Formula

Wave Speed = Propagation Velocity/sqrt([g]*Coastal Mean Depth)
v = v_p'/sqrt([g]*d)

What is Wave Number?

Wave Number is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance.

How to Calculate Dimensionless Wave Speed?

Dimensionless Wave Speed calculator uses Wave Speed = Propagation Velocity/sqrt([g]*Coastal Mean Depth) to calculate the Wave Speed, The Dimensionless Wave Speed is defined as how fast the wave travels and is determined by the properties of the medium in which the wave is moving. Wave Speed is denoted by v symbol.

How to calculate Dimensionless Wave Speed using this online calculator? To use this online calculator for Dimensionless Wave Speed, enter Propagation Velocity (v_p') & Coastal Mean Depth (d) and hit the calculate button. Here is how the Dimensionless Wave Speed calculation can be explained with given input values -> 50.00579 = 495.2/sqrt([g]*10).

FAQ

What is Dimensionless Wave Speed?

The Dimensionless Wave Speed is defined as how fast the wave travels and is determined by the properties of the medium in which the wave is moving and is represented as v = v_p'/sqrt([g]*d) or Wave Speed = Propagation Velocity/sqrt([g]*Coastal Mean Depth). Propagation Velocity refers to the speed at which waves or other disturbances propagate through water & Coastal Mean Depth is the average water depth over a particular area, such as a section of coastline, a bay, or an ocean basin.

How to calculate Dimensionless Wave Speed?

The Dimensionless Wave Speed is defined as how fast the wave travels and is determined by the properties of the medium in which the wave is moving is calculated using Wave Speed = Propagation Velocity/sqrt([g]*Coastal Mean Depth). To calculate Dimensionless Wave Speed, you need Propagation Velocity (v_p') & Coastal Mean Depth (d). With our tool, you need to enter the respective value for Propagation Velocity & Coastal Mean Depth and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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