Radian Frequency of Wave Calculator

✖Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance.ⓘ Wave Number for Water Wave [k]			+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%

✖Angular Frequency of Wave is the rate of change of phase of a sinusoidal waveform, typically measured in radians per second.ⓘ Radian Frequency of Wave [ω_c]

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Formula

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Radian Frequency of Wave

Formula

`"ω"_{"c"} = sqrt("[g]"*"k"*tanh("k"*"d"))`

Example

`"1.375055rad/s"=sqrt("[g]"*"0.2"*tanh("0.2"*"10m"))`

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Radian Frequency of Wave Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Frequency of Wave = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Coastal Mean Depth))
ω_c = sqrt([g]*k*tanh(k*d))
This formula uses 1 Constants, 2 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)
tanh - The hyperbolic tangent function (tanh) is a function that is defined as the ratio of the hyperbolic sine function (sinh) to the hyperbolic cosine function (cosh)., tanh(Number)

Variables Used

Angular Frequency of Wave - (Measured in Radian per Second) - Angular Frequency of Wave is the rate of change of phase of a sinusoidal waveform, typically measured in radians per second.
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.
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

Wave Number for Water Wave: 0.2 --> No Conversion Required
Coastal Mean Depth: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_c = sqrt([g]*k*tanh(k*d)) --> sqrt([g]*0.2*tanh(0.2*10))

Evaluating ... ...

ω_c = 1.37505498567516

STEP 3: Convert Result to Output's Unit

1.37505498567516 Radian per Second --> No Conversion Required

FINAL ANSWER

1.37505498567516 ≈ 1.375055 Radian per Second <-- Angular Frequency of Wave

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surface Gravity Waves » Linear Dispersion Relation of Linear Wave » Radian Frequency of Wave

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

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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

Radian Frequency of Wave Formula

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

What is Wave Period?

The Wave Period is the time it takes to complete one cycle. The standard unit of a wave period is in seconds, and it is inversely proportional to the frequency of a wave, which is the number of cycles of waves that occur in one second. In other words, the higher the frequency of a wave, the lower the wave period.

How to Calculate Radian Frequency of Wave?

Radian Frequency of Wave calculator uses Angular Frequency of Wave = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Coastal Mean Depth)) to calculate the Angular Frequency of Wave, The Radian frequency of wave is defined as the angular displacement per unit time. Angular Frequency of Wave is denoted by ω_c symbol.

How to calculate Radian Frequency of Wave using this online calculator? To use this online calculator for Radian Frequency of Wave, enter Wave Number for Water Wave (k) & Coastal Mean Depth (d) and hit the calculate button. Here is how the Radian Frequency of Wave calculation can be explained with given input values -> 1.375055 = sqrt([g]*0.2*tanh(0.2*10)).

FAQ

What is Radian Frequency of Wave?

The Radian frequency of wave is defined as the angular displacement per unit time and is represented as ω_c = sqrt([g]*k*tanh(k*d)) or Angular Frequency of Wave = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Coastal Mean Depth)). Wave Number for Water Wave represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance & 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 Radian Frequency of Wave?

The Radian frequency of wave is defined as the angular displacement per unit time is calculated using Angular Frequency of Wave = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Coastal Mean Depth)). To calculate Radian Frequency of Wave, you need Wave Number for Water Wave (k) & Coastal Mean Depth (d). With our tool, you need to enter the respective value for Wave Number for Water Wave & 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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