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Eckart's Equation for Wavelength Formula

GoWavelength given Maximum Wave Steepness Limit by Michell Formula

GoWavelength for Maximum Wave Steepness Formula

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Wavelength can be defined as the distance between two successive crests or troughs of a wave. Check FAQs

λ = (([g] \cdot \frac{P^{2}}{2} \cdot π) \cdot \sqrt{\frac{\tanh (4 \cdot π^{2} \cdot d)}{P^{2}} \cdot [g]})

λ - Wavelength?P - Wave Period?d - Water Depth?[g] - Gravitational acceleration on Earth?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Eckart's Equation for Wavelength Example

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Here is how the Eckart's Equation for Wavelength equation looks like with Values.

Here is how the Eckart's Equation for Wavelength equation looks like with Units.

Here is how the Eckart's Equation for Wavelength equation looks like.

49.6865 = ((9.8066 \cdot \frac{{1.03}^{2}}{2} \cdot 3.1416) \cdot \sqrt{\frac{\tanh (4 \cdot {3.1416}^{2} \cdot 0.91)}{{1.03}^{2}} \cdot 9.8066})

49.6865m = ((9.8066m/s² \cdot \frac{{1.03}^{2}}{2} \cdot 3.1416) \cdot \sqrt{\frac{\tanh (4 \cdot {3.1416}^{2} \cdot 0.91m)}{{1.03}^{2}} \cdot 9.8066m/s²})

49.6865 = ((9.8066 \cdot \frac{{1.03}^{2}}{2} \cdot 3.1416) \cdot \sqrt{\frac{\tanh (4 \cdot {3.1416}^{2} \cdot 0.91)}{{1.03}^{2}} \cdot 9.8066})

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Eckart's Equation for Wavelength Solution

Follow our step by step solution on how to calculate Eckart's Equation for Wavelength?

FIRST Step Consider the formula

λ = (([g] \cdot \frac{P^{2}}{2} \cdot π) \cdot \sqrt{\frac{\tanh (4 \cdot π^{2} \cdot d)}{P^{2}} \cdot [g]})

Next Step Substitute values of Variables

∴

λ = (([g] \cdot \frac{{1.03}^{2}}{2} \cdot π) \cdot \sqrt{\frac{\tanh (4 \cdot π^{2} \cdot 0.91m)}{{1.03}^{2}} \cdot [g]})

Next Step Substitute values of Constants

∴

λ = ((9.8066m/s² \cdot \frac{{1.03}^{2}}{2} \cdot 3.1416) \cdot \sqrt{\frac{\tanh (4 \cdot {3.1416}^{2} \cdot 0.91m)}{{1.03}^{2}} \cdot 9.8066m/s²})

Next Step Prepare to Evaluate

∴

λ = ((9.8066 \cdot \frac{{1.03}^{2}}{2} \cdot 3.1416) \cdot \sqrt{\frac{\tanh (4 \cdot {3.1416}^{2} \cdot 0.91)}{{1.03}^{2}} \cdot 9.8066})

Next Step Evaluate

∴

λ = 49.6864667882897m

LAST Step Rounding Answer

∴

λ = 49.6865m

Eckart's Equation for Wavelength Formula Elements

Variables

Constants

Functions

Wavelength

Wavelength can be defined as the distance between two successive crests or troughs of a wave.

Symbol: λ

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wavelength

Wave Period

Wave Period is the time between successive peaks or troughs.

Symbol: P

Measurement: NAUnit: Unitless

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 can be positive or negative.

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

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

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 to find Wavelength

Go Wavelength given Maximum Wave Steepness Limit by Michell

λ = \frac{H}{0.142}

Go Wavelength for Maximum Wave Steepness

λ = 2 \cdot π \cdot \frac{d}{a} \tanh (\frac{ε s}{0.142})

Other formulas in Wave Parameters category

Go Wave Amplitude

a = \frac{H}{2}

Go Angular of Radian Frequency of Wave

ω = 2 \cdot \frac{π}{P}

Go Wave number given wavelength

k = 2 \cdot \frac{π}{λ}

Go Phase Velocity or Wave Celerity

C = \frac{λ}{P}

How to Evaluate Eckart's Equation for Wavelength?

Eckart's Equation for Wavelength evaluator uses Wavelength = (([g]*Wave Period^2/2*pi)*sqrt(tanh(4*pi^2*Water Depth)/Wave Period^2*[g])) to evaluate the Wavelength, The Eckart's Equation for Wavelength formula is defined as the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space. Wavelength is denoted by λ symbol.

How to evaluate Eckart's Equation for Wavelength using this online evaluator? To use this online evaluator for Eckart's Equation for Wavelength, enter Wave Period (P) & Water Depth (d) and hit the calculate button.

FAQs on Eckart's Equation for Wavelength

What is the formula to find Eckart's Equation for Wavelength?

The formula of Eckart's Equation for Wavelength is expressed as Wavelength = (([g]*Wave Period^2/2*pi)*sqrt(tanh(4*pi^2*Water Depth)/Wave Period^2*[g])). Here is an example- 49.68647 = (([g]*1.03^2/2*pi)*sqrt(tanh(4*pi^2*0.91)/1.03^2*[g])).

How to calculate Eckart's Equation for Wavelength?

With Wave Period (P) & Water Depth (d) we can find Eckart's Equation for Wavelength using the formula - Wavelength = (([g]*Wave Period^2/2*pi)*sqrt(tanh(4*pi^2*Water Depth)/Wave Period^2*[g])). This formula also uses Gravitational acceleration on Earth, Gravitational acceleration on Earth, Archimedes' constant and , Square Root (sqrt), Hyperbolic Tangent (tanh) function(s).

What are the other ways to Calculate Wavelength?

Here are the different ways to Calculate Wavelength-

Wavelength=Wave Height/0.142
Wavelength=2*pi*Water Depth/atanh(Wave Steepness/0.142)

Can the Eckart's Equation for Wavelength be negative?

Yes, the Eckart's Equation for Wavelength, measured in Length can be negative.

Which unit is used to measure Eckart's Equation for Wavelength?

Eckart's Equation for Wavelength is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Eckart's Equation for Wavelength can be measured.

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