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Water Depth given Wavelength, Wave Period and Wave Number Formula

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

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

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

Water Depth given Wavelength, Wave Period and Wave Number Example

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

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

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

2.1575 = \frac{a \tanh (\frac{0.4 \cdot 6.2}{9.8066 \cdot 0.622})}{0.2}

2.1575m = \frac{a \tanh (\frac{0.4m \cdot 6.2rad/s}{9.8066m/s² \cdot 0.622s})}{0.2}

2.1575 = \frac{a \tanh (\frac{0.4 \cdot 6.2}{9.8066 \cdot 0.622})}{0.2}

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Water Depth given Wavelength, Wave Period and Wave Number Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d = \frac{a \tanh (\frac{0.4m \cdot 6.2rad/s}{[g] \cdot 0.622s})}{0.2}

Next Step Substitute values of Constants

∴

d = \frac{a \tanh (\frac{0.4m \cdot 6.2rad/s}{9.8066m/s² \cdot 0.622s})}{0.2}

Next Step Prepare to Evaluate

∴

d = \frac{a \tanh (\frac{0.4 \cdot 6.2}{9.8066 \cdot 0.622})}{0.2}

Next Step Evaluate

∴

d = 2.15750500220341m

LAST Step Rounding Answer

∴

d = 2.1575m

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

Variables

Constants

Functions

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

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

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

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 Wave Number given Wavelength, Wave Period and Water Depth

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

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]}

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

Water Depth given Wavelength, Wave Period and Wave Number evaluator uses Water Depth = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Wave Number for Water Wave to evaluate the Water Depth, The Water Depth given Wavelength, Wave Period and Wave Number formula is defined as the vertical distance from the water surface to the seabed, determined by the wavelength, wave period, and wave number of a propagating wave. Water Depth is denoted by d symbol.

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

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

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

The formula of Water Depth given Wavelength, Wave Period and Wave Number is expressed as Water Depth = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Wave Number for Water Wave. Here is an example- 2.157505 = (atanh((0.4*6.2)/([g]*0.622)))/0.2.

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

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

Can the Water Depth given Wavelength, Wave Period and Wave Number be negative?

No, the Water Depth given Wavelength, Wave Period and Wave Number, measured in Length cannot be negative.

Which unit is used to measure Water Depth given Wavelength, Wave Period and Wave Number?

Water Depth given Wavelength, Wave Period and Wave Number is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Water Depth given Wavelength, Wave Period and Wave Number can be measured.

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Water Depth given Wavelength, Wave Period and Wave Number Formula

Water Depth given Wavelength, Wave Period and Wave Number Example

Water Depth given Wavelength, Wave Period and Wave Number Solution

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

Other formulas in Predicting Waves in Deep Water category

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

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

Variable Name