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Angular Frequency of Wave Formula

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Angular Frequency of Wave is the rate of change of phase of a sinusoidal waveform, typically measured in radians per second. Check FAQs

ω c = \sqrt{[g] \cdot k \cdot \tanh (k \cdot d)}

ω_c - Angular Frequency of Wave?k - Wave Number for Water Wave?d - Coastal Mean Depth?[g] - Gravitational acceleration on Earth?

Angular Frequency of Wave Example

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Here is how the Angular Frequency of Wave equation looks like with Values.

Here is how the Angular Frequency of Wave equation looks like with Units.

Here is how the Angular Frequency of Wave equation looks like.

1.3751 = \sqrt{9.8066 \cdot 0.2 \cdot \tanh (0.2 \cdot 10)}

1.3751rad/s = \sqrt{9.8066m/s² \cdot 0.2 \cdot \tanh (0.2 \cdot 10m)}

1.3751 = \sqrt{9.8066 \cdot 0.2 \cdot \tanh (0.2 \cdot 10)}

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Angular Frequency of Wave Solution

Follow our step by step solution on how to calculate Angular Frequency of Wave?

FIRST Step Consider the formula

ω c = \sqrt{[g] \cdot k \cdot \tanh (k \cdot d)}

Next Step Substitute values of Variables

∴

ω c = \sqrt{[g] \cdot 0.2 \cdot \tanh (0.2 \cdot 10m)}

Next Step Substitute values of Constants

∴

ω c = \sqrt{9.8066m/s² \cdot 0.2 \cdot \tanh (0.2 \cdot 10m)}

Next Step Prepare to Evaluate

∴

ω c = \sqrt{9.8066 \cdot 0.2 \cdot \tanh (0.2 \cdot 10)}

Next Step Evaluate

∴

ω c = 1.37505498567516rad/s

LAST Step Rounding Answer

∴

ω c = 1.3751rad/s

Angular Frequency of Wave Formula Elements

Variables

Constants

Functions

Angular Frequency of Wave

Angular Frequency of Wave is the rate of change of phase of a sinusoidal waveform, typically measured in radians per second.

Symbol: ω_c

Measurement: Angular FrequencyUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Frequency of Wave

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

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

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.

Syntax: 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).

Syntax: tanh(Number)

Other formulas in Linear Dispersion Relation of Linear Wave category

Go Velocity of Propagation in Linear Dispersion Relation

C v = \sqrt{\frac{[g] \cdot d \cdot \tanh (k \cdot d)}{k \cdot d}}

Go Wavelength given Wave Number

λ'' = \frac{2 \cdot π}{k}

Go Relative Wavelength

λ r = \frac{λ o}{d}

Go Velocity of Propagation in Linear Dispersion Relation given Wavelength

C v = \sqrt{\frac{[g] \cdot d \cdot \tanh (2 \cdot π \cdot \frac{d}{λ''})}{2 \cdot π \cdot \frac{d}{λ''}}}

How to Evaluate Angular Frequency of Wave?

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

How to evaluate Angular Frequency of Wave using this online evaluator? To use this online evaluator for Angular Frequency of Wave, enter Wave Number for Water Wave (k) & Coastal Mean Depth (d) and hit the calculate button.

FAQs on Angular Frequency of Wave

What is the formula to find Angular Frequency of Wave?

The formula of Angular Frequency of Wave is expressed as Angular Frequency of Wave = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Coastal Mean Depth)). Here is an example- 1.375055 = sqrt([g]*0.2*tanh(0.2*10)).

How to calculate Angular Frequency of Wave?

With Wave Number for Water Wave (k) & Coastal Mean Depth (d) we can find Angular Frequency of Wave using the formula - Angular Frequency of Wave = sqrt([g]*Wave Number for Water Wave*tanh(Wave Number for Water Wave*Coastal Mean Depth)). This formula also uses Gravitational acceleration on Earth constant(s) and , Square Root (sqrt), Hyperbolic Tangent (tanh) function(s).

Can the Angular Frequency of Wave be negative?

No, the Angular Frequency of Wave, measured in Angular Frequency cannot be negative.

Which unit is used to measure Angular Frequency of Wave?

Angular Frequency of Wave is usually measured using the Radian per Second[rad/s] for Angular Frequency. Degree per Second[rad/s] are the few other units in which Angular Frequency of Wave can be measured.

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