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Wave Number given Wavelength, Wave Period and Water Depth Formula

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The Wave Number for Water Waves quantifies the number of waves per unit length along the surface of the water. Check FAQs

k = \frac{a \tanh (\frac{L \cdot ω}{[g] \cdot T})}{d}

k - Wave Number for Water Wave?L - Wavelength?ω - Wave Angular Frequency?T - Wave Period?d - Water Depth?[g] - Gravitational acceleration on Earth?

Wave Number given Wavelength, Wave Period and Water Depth Example

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Here is how the Wave Number given Wavelength, Wave Period and Water Depth equation looks like with Values.

Here is how the Wave Number given Wavelength, Wave Period and Water Depth equation looks like with Units.

Here is how the Wave Number given Wavelength, Wave Period and Water Depth equation looks like.

0.2007 = \frac{a \tanh (\frac{0.4 \cdot 6.2}{9.8066 \cdot 0.622})}{2.15}

0.2007 = \frac{a \tanh (\frac{0.4m \cdot 6.2rad/s}{9.8066m/s² \cdot 0.622s})}{2.15m}

0.2007 = \frac{a \tanh (\frac{0.4 \cdot 6.2}{9.8066 \cdot 0.622})}{2.15}

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Wave Number given Wavelength, Wave Period and Water Depth Solution

Follow our step by step solution on how to calculate Wave Number given Wavelength, Wave Period and Water Depth?

FIRST Step Consider the formula

k = \frac{a \tanh (\frac{L \cdot ω}{[g] \cdot T})}{d}

Next Step Substitute values of Variables

∴

k = \frac{a \tanh (\frac{0.4m \cdot 6.2rad/s}{[g] \cdot 0.622s})}{2.15m}

Next Step Substitute values of Constants

∴

k = \frac{a \tanh (\frac{0.4m \cdot 6.2rad/s}{9.8066m/s² \cdot 0.622s})}{2.15m}

Next Step Prepare to Evaluate

∴

k = \frac{a \tanh (\frac{0.4 \cdot 6.2}{9.8066 \cdot 0.622})}{2.15}

Next Step Evaluate

∴

k = 0.200698139739852

LAST Step Rounding Answer

∴

k = 0.2007

Wave Number given Wavelength, Wave Period and Water Depth Formula Elements

Variables

Constants

Functions

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.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wave Number for Water Wave

Wavelength

Wavelength is the distance between successive crests, troughs, or any corresponding points on a wave.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Wavelength

Wave Angular Frequency

Wave Angular Frequency is the rate of change of the phase of the wave over time, given by the symbol ω (omega).

Symbol: ω

Measurement: Angular FrequencyUnit: rad/s

Note: Value can be positive or negative.

Formulas to find Wave Angular Frequency

Wave Period

Wave Period is the time it takes for successive wave crests or troughs to pass a fixed point.

Symbol: T

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Wave Period

Water Depth

Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water 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

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)

atanh

The inverse hyperbolic tangent function returns the value whose hyperbolic tangent is a number.

Syntax: atanh(Number)

Other formulas in Predicting Waves in Deep Water category

Go Significant Wave Height from Bretschneider Empirical Relationships

H dw = \frac{U^{2} \cdot 0.283 \cdot \tanh (0.0125 \cdot {(\frac{[g] \cdot F l}{U^{2}})}^{0.42})}{[g]}

Go Significant Wave Period from Bretschneider Empirical Relationships

T = \frac{U \cdot 7.54 \cdot \tanh (0.077 \cdot {(\frac{[g] \cdot F l}{U^{2}})}^{0.25})}{[g]}

Go Water Depth given Wavelength, Wave Period and Wave Number

d = \frac{a \tanh (\frac{L \cdot ω}{[g] \cdot T})}{k}

How to Evaluate Wave Number given Wavelength, Wave Period and Water Depth?

Wave Number given Wavelength, Wave Period and Water Depth evaluator uses Wave Number for Water Wave = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Water Depth to evaluate the Wave Number for Water Wave, The Wave Number given Wavelength, Wave Period and Water Depth formula is defined as the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Wave Number for Water Wave is denoted by k symbol.

How to evaluate Wave Number given Wavelength, Wave Period and Water Depth using this online evaluator? To use this online evaluator for Wave Number given Wavelength, Wave Period and Water Depth, enter Wavelength (L), Wave Angular Frequency (ω), Wave Period (T) & Water Depth (d) and hit the calculate button.

FAQs on Wave Number given Wavelength, Wave Period and Water Depth

What is the formula to find Wave Number given Wavelength, Wave Period and Water Depth?

The formula of Wave Number given Wavelength, Wave Period and Water Depth is expressed as Wave Number for Water Wave = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Water Depth. Here is an example- 0.200698 = (atanh((0.4*6.2)/([g]*0.622)))/2.15.

How to calculate Wave Number given Wavelength, Wave Period and Water Depth?

With Wavelength (L), Wave Angular Frequency (ω), Wave Period (T) & Water Depth (d) we can find Wave Number given Wavelength, Wave Period and Water Depth using the formula - Wave Number for Water Wave = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Water Depth. This formula also uses Gravitational acceleration on Earth constant(s) and , Hyperbolic Tangent (tanh), Inverse Hyperbolic Tangent (atanh) function(s).

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Wave Number given Wavelength, Wave Period and Water Depth Formula

Wave Number given Wavelength, Wave Period and Water Depth Example

Wave Number given Wavelength, Wave Period and Water Depth Solution

Wave Number given Wavelength, Wave Period and Water Depth Formula Elements

Other formulas in Predicting Waves in Deep Water category

How to Evaluate Wave Number given Wavelength, Wave Period and Water Depth?

FAQs on Wave Number given Wavelength, Wave Period and Water Depth

Variable Name