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Wavelength for Distance from Bottom to Wave Trough Formula

GoWavelength for Complete Elliptic Integral of First Kind Formula

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Wavelength of Wave refers to the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Check FAQs

λ = \sqrt{\frac{16 \cdot {d c}^{2} \cdot K k \cdot (K k - E k)}{3 \cdot ((\frac{y t}{d c}) + (\frac{H w}{d c}) - 1)}}

λ - Wavelength of Wave?d_c - Water Depth for Cnoidal Wave?K_k - Complete Elliptic Integral of the First Kind?E_k - Complete Elliptic Integral of the Second Kind?y_t - Distance from the Bottom to the Wave Trough?H_w - Height of the Wave?

Wavelength for Distance from Bottom to Wave Trough Example

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Here is how the Wavelength for Distance from Bottom to Wave Trough equation looks like with Values.

Here is how the Wavelength for Distance from Bottom to Wave Trough equation looks like with Units.

Here is how the Wavelength for Distance from Bottom to Wave Trough equation looks like.

32.0964 = \sqrt{\frac{16 \cdot 16^{2} \cdot 28 \cdot (28 - 27.968)}{3 \cdot ((\frac{21}{16}) + (\frac{14}{16}) - 1)}}

32.0964m = \sqrt{\frac{16 \cdot {16m}^{2} \cdot 28 \cdot (28 - 27.968)}{3 \cdot ((\frac{21m}{16m}) + (\frac{14m}{16m}) - 1)}}

32.0964 = \sqrt{\frac{16 \cdot 16^{2} \cdot 28 \cdot (28 - 27.968)}{3 \cdot ((\frac{21}{16}) + (\frac{14}{16}) - 1)}}

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Wavelength for Distance from Bottom to Wave Trough Solution

Follow our step by step solution on how to calculate Wavelength for Distance from Bottom to Wave Trough?

FIRST Step Consider the formula

λ = \sqrt{\frac{16 \cdot {d c}^{2} \cdot K k \cdot (K k - E k)}{3 \cdot ((\frac{y t}{d c}) + (\frac{H w}{d c}) - 1)}}

Next Step Substitute values of Variables

∴

λ = \sqrt{\frac{16 \cdot {16m}^{2} \cdot 28 \cdot (28 - 27.968)}{3 \cdot ((\frac{21m}{16m}) + (\frac{14m}{16m}) - 1)}}

Next Step Prepare to Evaluate

∴

λ = \sqrt{\frac{16 \cdot 16^{2} \cdot 28 \cdot (28 - 27.968)}{3 \cdot ((\frac{21}{16}) + (\frac{14}{16}) - 1)}}

Next Step Evaluate

∴

λ = 32.0964161523458m

LAST Step Rounding Answer

∴

λ = 32.0964m

Wavelength for Distance from Bottom to Wave Trough Formula Elements

Variables

Functions

Wavelength of Wave

Wavelength of Wave refers to the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings.

Symbol: λ

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wavelength of Wave

Water Depth for Cnoidal Wave

Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.

Symbol: d_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth for Cnoidal Wave

Complete Elliptic Integral of the First Kind

Complete Elliptic Integral of the First Kind is a mathematical tool that finds applications in coastal and ocean engineering, particularly in wave theory and harmonic analysis of wave data.

Symbol: K_k

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Complete Elliptic Integral of the First Kind

Complete Elliptic Integral of the Second Kind

Complete Elliptic Integral of the Second Kind influencing the wavelength and the distance from bottom to wave trough.

Symbol: E_k

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Complete Elliptic Integral of the Second Kind

Distance from the Bottom to the Wave Trough

Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.

Symbol: y_t

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance from the Bottom to the Wave Trough

Height of the Wave

Height of the Wave is the difference between the elevations of a crest and a neighboring trough.

Symbol: H_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Height of the Wave

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)

Other Formulas to find Wavelength of Wave

Go Wavelength for Complete Elliptic Integral of First Kind

λ = \sqrt{16 \cdot \frac{{d c}^{3}}{3 \cdot H w}} \cdot k \cdot K k

Other formulas in Cnoidal Wave Theory category

Go Distance from Bottom to Wave Trough

y t = d c \cdot ((\frac{y c}{d c}) - (\frac{H w}{d c}))

Go Distance from Bottom to Crest

y c = d c \cdot ((\frac{y t}{d c}) + (\frac{H w}{d c}))

Go Trough to Crest Wave Height

H w = d c \cdot ((\frac{y c}{d c}) - (\frac{y t}{d c}))

Go Complete Elliptic Integral of Second Kind

E k = - ((((\frac{y t}{d c}) + (\frac{H w}{d c}) - 1) \cdot \frac{3 \cdot λ^{2}}{(16 \cdot {d c}^{2}) \cdot K k}) - K k)

How to Evaluate Wavelength for Distance from Bottom to Wave Trough?

Wavelength for Distance from Bottom to Wave Trough evaluator uses Wavelength of Wave = sqrt((16*Water Depth for Cnoidal Wave^2*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind))/(3*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of the Wave/Water Depth for Cnoidal Wave)-1))) to evaluate the Wavelength of Wave, The Wavelength for Distance from Bottom to Wave Trough formula is defined as the spatial period of a periodic waves i.e. the distance over which the wave's shape repeats. Wavelength of Wave is denoted by λ symbol.

How to evaluate Wavelength for Distance from Bottom to Wave Trough using this online evaluator? To use this online evaluator for Wavelength for Distance from Bottom to Wave Trough, enter Water Depth for Cnoidal Wave (d_c), Complete Elliptic Integral of the First Kind (K_k), Complete Elliptic Integral of the Second Kind (E_k), Distance from the Bottom to the Wave Trough (y_t) & Height of the Wave (H_w) and hit the calculate button.

FAQs on Wavelength for Distance from Bottom to Wave Trough

What is the formula to find Wavelength for Distance from Bottom to Wave Trough?

The formula of Wavelength for Distance from Bottom to Wave Trough is expressed as Wavelength of Wave = sqrt((16*Water Depth for Cnoidal Wave^2*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind))/(3*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of the Wave/Water Depth for Cnoidal Wave)-1))). Here is an example- 32.09642 = sqrt((16*16^2*28*(28-27.968))/(3*((21/16)+(14/16)-1))).

How to calculate Wavelength for Distance from Bottom to Wave Trough?

With Water Depth for Cnoidal Wave (d_c), Complete Elliptic Integral of the First Kind (K_k), Complete Elliptic Integral of the Second Kind (E_k), Distance from the Bottom to the Wave Trough (y_t) & Height of the Wave (H_w) we can find Wavelength for Distance from Bottom to Wave Trough using the formula - Wavelength of Wave = sqrt((16*Water Depth for Cnoidal Wave^2*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind))/(3*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of the Wave/Water Depth for Cnoidal Wave)-1))). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Wavelength of Wave?

Here are the different ways to Calculate Wavelength of Wave-

Wavelength of Wave=sqrt(16*Water Depth for Cnoidal Wave^3/(3*Height of the Wave))*Modulus of the Elliptic Integrals*Complete Elliptic Integral of the First Kind

Can the Wavelength for Distance from Bottom to Wave Trough be negative?

Yes, the Wavelength for Distance from Bottom to Wave Trough, measured in Length can be negative.

Which unit is used to measure Wavelength for Distance from Bottom to Wave Trough?

Wavelength for Distance from Bottom to Wave Trough is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Wavelength for Distance from Bottom to Wave Trough can be measured.

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Wavelength for Distance from Bottom to Wave Trough Formula

​GoWavelength for Complete Elliptic Integral of First Kind Formula

Wavelength for Distance from Bottom to Wave Trough Example

Wavelength for Distance from Bottom to Wave Trough Solution

Wavelength for Distance from Bottom to Wave Trough Formula Elements

Other Formulas to find Wavelength of Wave

Other formulas in Cnoidal Wave Theory category

How to Evaluate Wavelength for Distance from Bottom to Wave Trough?

FAQs on Wavelength for Distance from Bottom to Wave Trough

Variable Name

GoWavelength for Complete Elliptic Integral of First Kind Formula