Wavelength for Complete Elliptic Integral of First Kind Calculator

✖Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.ⓘ Water Depth for Cnoidal Wave [d_c]			+10% -10%
✖Height of the Wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Height of the Wave [H_w]			+10% -10%
✖Modulus of the Elliptic Integrals is essential for accurately modeling wave behavior, which is critical for designing coastal structures, assessing coastal hazards, and predicting wave impacts.ⓘ Modulus of the Elliptic Integrals [k]			+10% -10%
✖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.ⓘ Complete Elliptic Integral of the First Kind [K_k]			+10% -10%

✖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.ⓘ Wavelength for Complete Elliptic Integral of First Kind [λ]

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Wavelength for Complete Elliptic Integral of First Kind Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
λ = sqrt(16*d_c^3/(3*H_w))*k*K_k
This formula uses 1 Functions, 5 Variables

Functions Used

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., sqrt(Number)

Variables Used

Wavelength of Wave - (Measured in Meter) - 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.
Water Depth for Cnoidal Wave - (Measured in Meter) - Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.
Height of the Wave - (Measured in Meter) - Height of the Wave is the difference between the elevations of a crest and a neighboring trough.
Modulus of the Elliptic Integrals - Modulus of the Elliptic Integrals is essential for accurately modeling wave behavior, which is critical for designing coastal structures, assessing coastal hazards, and predicting wave impacts.
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.

STEP 1: Convert Input(s) to Base Unit

Water Depth for Cnoidal Wave: 16 Meter --> 16 Meter No Conversion Required
Height of the Wave: 14 Meter --> 14 Meter No Conversion Required
Modulus of the Elliptic Integrals: 0.0296 --> No Conversion Required
Complete Elliptic Integral of the First Kind: 28 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ = sqrt(16*d_c^3/(3*H_w))*k*K_k --> sqrt(16*16^3/(3*14))*0.0296*28

Evaluating ... ...

λ = 32.7389738108369

STEP 3: Convert Result to Output's Unit

32.7389738108369 Meter --> No Conversion Required

FINAL ANSWER

32.7389738108369 ≈ 32.73897 Meter <-- Wavelength of Wave

(Calculation completed in 00.020 seconds)

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< Cnoidal Wave Theory Calculators

Complete Elliptic Integral of Second Kind

LaTeX Go Complete Elliptic Integral of the Second Kind = -((((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of the Wave/Water Depth for Cnoidal Wave)-1)*(3*Wavelength of Wave^2)/((16*Water Depth for Cnoidal Wave^2)*Complete Elliptic Integral of the First Kind))-Complete Elliptic Integral of the First Kind)

Distance from Bottom to Wave Trough

LaTeX Go Distance from the Bottom to the Wave Trough = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Height of the Wave/Water Depth for Cnoidal Wave))

Distance from Bottom to Crest

LaTeX Go Distance from the Bottom to the Crest = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of the Wave/Water Depth for Cnoidal Wave))

Trough to Crest Wave Height

LaTeX Go Height of the Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave))

Wavelength for Complete Elliptic Integral of First Kind Formula

LaTeX Go

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
λ = sqrt(16*d_c^3/(3*H_w))*k*K_k

What Causes Waves?

Waves are most commonly caused by wind. Wind-driven waves, or surface waves, are created by the friction between wind and surface water. As wind blows across the surface of the ocean or a lake, the continual disturbance creates a wave crest. The gravitational pull of the sun and moon on the earth also causes waves.

How to Calculate Wavelength for Complete Elliptic Integral of First Kind?

Wavelength for Complete Elliptic Integral of First Kind calculator uses 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 to calculate the Wavelength of Wave, The Wavelength for Complete Elliptic Integral of First Kind 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 calculate Wavelength for Complete Elliptic Integral of First Kind using this online calculator? To use this online calculator for Wavelength for Complete Elliptic Integral of First Kind, enter Water Depth for Cnoidal Wave (d_c), Height of the Wave (H_w), Modulus of the Elliptic Integrals (k) & Complete Elliptic Integral of the First Kind (K_k) and hit the calculate button. Here is how the Wavelength for Complete Elliptic Integral of First Kind calculation can be explained with given input values -> 32.73897 = sqrt(16*16^3/(3*14))*0.0296*28.

FAQ

What is Wavelength for Complete Elliptic Integral of First Kind?

The Wavelength for Complete Elliptic Integral of First Kind formula is defined as the spatial period of a periodic waves i.e. the distance over which the wave's shape repeats and is represented as λ = sqrt(16*d_c^3/(3*H_w))*k*K_k or 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. Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating, Height of the Wave is the difference between the elevations of a crest and a neighboring trough, Modulus of the Elliptic Integrals is essential for accurately modeling wave behavior, which is critical for designing coastal structures, assessing coastal hazards, and predicting wave impacts & 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.

How to calculate Wavelength for Complete Elliptic Integral of First Kind?

The Wavelength for Complete Elliptic Integral of First Kind formula is defined as the spatial period of a periodic waves i.e. the distance over which the wave's shape repeats is calculated using 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. To calculate Wavelength for Complete Elliptic Integral of First Kind, you need Water Depth for Cnoidal Wave (d_c), Height of the Wave (H_w), Modulus of the Elliptic Integrals (k) & Complete Elliptic Integral of the First Kind (K_k). With our tool, you need to enter the respective value for Water Depth for Cnoidal Wave, Height of the Wave, Modulus of the Elliptic Integrals & Complete Elliptic Integral of the First Kind and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Wavelength of Wave?

In this formula, Wavelength of Wave uses Water Depth for Cnoidal Wave, Height of the Wave, Modulus of the Elliptic Integrals & Complete Elliptic Integral of the First Kind. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)))

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