Wavelength for Distance from Bottom to Wave Trough 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%
✖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%
✖Complete Elliptic Integral of the Second Kind influencing the wavelength and the distance from bottom to wave trough.ⓘ Complete Elliptic Integral of the Second Kind [E_k]			+10% -10%
✖Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.ⓘ Distance from the Bottom to the Wave Trough [y_t]			+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%

✖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 Distance from Bottom to Wave Trough [λ]

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Wavelength for Distance from Bottom to Wave Trough Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
λ = sqrt((16*d_c^2*K_k*(K_k-E_k))/(3*((y_t/d_c)+(H_w/d_c)-1)))
This formula uses 1 Functions, 6 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.
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.
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.
Distance from the Bottom to the Wave Trough - (Measured in Meter) - Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.
Height of the Wave - (Measured in Meter) - Height of the Wave is the difference between the elevations of a crest and a neighboring trough.

STEP 1: Convert Input(s) to Base Unit

Water Depth for Cnoidal Wave: 16 Meter --> 16 Meter No Conversion Required
Complete Elliptic Integral of the First Kind: 28 --> No Conversion Required
Complete Elliptic Integral of the Second Kind: 27.968 --> No Conversion Required
Distance from the Bottom to the Wave Trough: 21 Meter --> 21 Meter No Conversion Required
Height of the Wave: 14 Meter --> 14 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ = sqrt((16*d_c^2*K_k*(K_k-E_k))/(3*((y_t/d_c)+(H_w/d_c)-1))) --> sqrt((16*16^2*28*(28-27.968))/(3*((21/16)+(14/16)-1)))

Evaluating ... ...

λ = 32.0964161523458

STEP 3: Convert Result to Output's Unit

32.0964161523458 Meter --> No Conversion Required

FINAL ANSWER

32.0964161523458 ≈ 32.09642 Meter <-- Wavelength of Wave

(Calculation completed in 00.020 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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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 Distance from Bottom to Wave Trough Formula

LaTeX Go

What are the Characteristics of Progressive Waves?

A progressive wave is formed due to continuous vibration of the particles of the medium.
The wave travels with a certain velocity.
There is a flow of energy in the direction of the wave.
No particles in the medium are at rest.
The amplitude of all the particles is the same.

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

Wavelength for Distance from Bottom to Wave Trough calculator 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 calculate 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 calculate Wavelength for Distance from Bottom to Wave Trough using this online calculator? To use this online calculator 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. Here is how the Wavelength for Distance from Bottom to Wave Trough calculation can be explained with given input values -> 32.09642 = sqrt((16*16^2*28*(28-27.968))/(3*((21/16)+(14/16)-1))).

FAQ

What is Wavelength for Distance from Bottom to Wave Trough?

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 and is represented as λ = sqrt((16*d_c^2*K_k*(K_k-E_k))/(3*((y_t/d_c)+(H_w/d_c)-1))) or 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))). Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating, 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 Second Kind influencing the wavelength and the distance from bottom to 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 & Height of the Wave is the difference between the elevations of a crest and a neighboring trough.

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

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 is calculated using 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 calculate Wavelength for Distance from Bottom to Wave Trough, you need 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). With our tool, you need to enter the respective value for Water Depth for Cnoidal Wave, Complete Elliptic Integral of the First Kind, Complete Elliptic Integral of the Second Kind, Distance from the Bottom to the Wave Trough & Height of the Wave 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, Complete Elliptic Integral of the First Kind, Complete Elliptic Integral of the Second Kind, Distance from the Bottom to the Wave Trough & Height of the Wave. 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^3/(3*Height of the Wave))*Modulus of the Elliptic Integrals*Complete Elliptic Integral of the First Kind

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