Radian Frequency of Wave Solution

STEP 0: Pre-Calculation Summary
Formula Used
Wave Angular Frequency = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Mean Depth))
ω = 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
Wave Angular Frequency - (Measured in Radian per Second) - Wave Angular Frequency angular displacement of the wave per unit time. Its units are therefore degrees (or radians) per second.
Wave Number for Water Wave - The wave number for water waves quantifies the number of waves per unit length along the surface of the water.
Mean Depth - (Measured in Meter) - Mean Depth for Steady two-dimensional waves.
STEP 1: Convert Input(s) to Base Unit
Wave Number for Water Wave: 0.2 --> No Conversion Required
Mean Depth: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ω = sqrt([g]*k*tanh(k*d)) --> sqrt([g]*0.2*tanh(0.2*10))
Evaluating ... ...
ω = 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 <-- Wave Angular Frequency
(Calculation completed in 00.004 seconds)

Credits

Created by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
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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]*Mean Depth*tanh(2*pi*Mean Depth/Deep-Water Wavelength))/(2*pi*Mean Depth/Deep-Water Wavelength))
Guo Formula of Linear Dispersion Relation for Wave Number
Go Wave Number for Water Wave = ((Wave Angular Frequency^2*Mean Depth)/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Mean Depth/[g])^(5/2))^(-2/5)))/Mean Depth
Guo Formula of Linear Dispersion Relation
Go Linear Dispersion Relation = (Wave Angular Frequency^2*Mean Depth/[g])*(1-exp(-(Wave Angular Frequency*sqrt(Mean Depth/[g])^(5/2))^(-2/5)))
Velocity of Propagation in Linear Dispersion Relation
Go Velocity of Propagation = sqrt(([g]*Mean Depth*tanh(Wave Number for Water Wave*Mean Depth))/(Wave Number for Water Wave*Mean Depth))
Wave Number of Convenient Empirical Explicit Approximation
Go Wave Number for Water Wave = (Wave Angular Frequency^2/[g])*(coth((Wave Angular Frequency*sqrt(Mean Depth/[g])^(3/2))^(2/3)))
Radian Frequency of Wave
Go Wave Angular Frequency = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Mean Depth))
Dimensionless Wave Speed
Go Wave Speed = Velocity of Propagation/sqrt([g]*Mean Depth)
Wave Number for Steady Two-dimensional Waves
Go Wave Number for Water Wave = (2*pi)/Deep-Water Wavelength
Wavelength given wave number
Go Deep-Water Wavelength = (2*pi)/Wave Number for Water Wave
Relative Wavelength
Go Relative Wavelength = Deep-Water Wavelength/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

Wave Angular Frequency = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Mean Depth))
ω = 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 Wave Angular Frequency = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Mean Depth)) to calculate the Wave Angular Frequency, The Radian frequency of wave also known as radial or circular frequency, measures angular displacement per unit time. Wave Angular Frequency is denoted by ω 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) & 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 also known as radial or circular frequency, measures angular displacement per unit time and is represented as ω = sqrt([g]*k*tanh(k*d)) or Wave Angular Frequency = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Mean Depth)). The wave number for water waves quantifies the number of waves per unit length along the surface of the water & Mean Depth for Steady two-dimensional waves.
How to calculate Radian Frequency of Wave?
The Radian frequency of wave also known as radial or circular frequency, measures angular displacement per unit time is calculated using Wave Angular Frequency = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Mean Depth)). To calculate Radian Frequency of Wave, you need Wave Number for Water Wave (k) & Mean Depth (d). With our tool, you need to enter the respective value for Wave Number for Water Wave & Mean Depth and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Wave Angular Frequency?
In this formula, Wave Angular Frequency uses Wave Number for Water Wave & Mean Depth. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Wave Angular Frequency = 2*pi/Wave Period
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