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*dc^2*Kk*(Kk-Ek))/(3*((yt/dc)+(Hw/dc)-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 can be defined as the distance between two successive crests or troughs of a wave.
Water Depth for Cnoidal Wave - (Measured in Meter) - Water Depth for Cnoidal Wave is the y depth from bed under cnoidal wave.
Complete Elliptic Integral of the first kind - 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.
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*dc^2*Kk*(Kk-Ek))/(3*((yt/dc)+(Hw/dc)-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 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg
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14 Cnoidal Wave Theory Calculators

Wavelength for Distance from Bottom to Wave Trough
Go 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)))
Complete Elliptic Integral of Second Kind
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)
Wave Height given Distance from Bottom to Wave Trough and Water Depth
Go Height of The Wave = -Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)-1-((16*Water Depth for Cnoidal Wave^2/(3*Wavelength of Wave^2))*Complete Elliptic Integral of the first kind*(Complete Elliptic Integral of the first kind-Complete Elliptic Integral of the Second Kind)))
Wave Height Required to Produce Difference in Pressure on Seabed
Go Height of The Wave = Change in Pressure/((Density of Salt Water*[g])*(0.5+(0.5*sqrt(1-((3*Change in Pressure)/(Density of Salt Water*[g]*Water Depth for Cnoidal Wave))))))
Free Surface Elevation of Solitary Waves
Go Free Surface Elevation = Height of The Wave*(Particle Velocity/(sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave)))
Particle Velocities given Free Surface Elevation of Solitary Waves
Go Particle Velocity = Free Surface Elevation*sqrt([g]*Water Depth for Cnoidal Wave)*(Height of The Wave/Water Depth for Cnoidal Wave)/Height of The Wave
Distance from Bottom to Wave Trough
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
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
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))
Wave Height when Free Surface Elevation of Solitary Waves
Go Height of The Wave = Free Surface Elevation*sqrt([g]*Water Depth for Cnoidal Wave)/(Particle Velocity*Water Depth for Cnoidal Wave)
Wavelength for Complete Elliptic Integral of First Kind
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
Elevation above Bottom given Pressure under Cnoidal Wave in Hydrostatic Form
Go Any Elevation above the Bottom = -((Pressure under A Wave/(Density of Salt Water*[g]))-Ordinate of the Water Surface)
Ordinate of Water Surface given Pressure under Cnoidal Wave in Hydrostatic Form
Go Ordinate of the Water Surface = (Pressure under A Wave/(Density of Salt Water*[g]))+Any Elevation above the Bottom
Pressure under Cnoidal Wave in Hydrostatic Form
Go Pressure under A Wave = Density of Salt Water*[g]*(Ordinate of the Water Surface-Any Elevation above the Bottom)

Wavelength for Distance from Bottom to Wave Trough 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)))
λ = sqrt((16*dc^2*Kk*(Kk-Ek))/(3*((yt/dc)+(Hw/dc)-1)))

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 is the spatial period of a periodic wave—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 (dc), Complete Elliptic Integral of the first kind (Kk), Complete Elliptic Integral of the Second Kind (Ek), Distance from the Bottom to the Wave Trough (yt) & Height of The Wave (Hw) 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 is the spatial period of a periodic wave—the distance over which the wave's shape repeats and is represented as λ = sqrt((16*dc^2*Kk*(Kk-Ek))/(3*((yt/dc)+(Hw/dc)-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 is the y depth from bed under cnoidal wave, Complete Elliptic Integral of the First 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 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 is the spatial period of a periodic wave—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 (dc), Complete Elliptic Integral of the first kind (Kk), Complete Elliptic Integral of the Second Kind (Ek), Distance from the Bottom to the Wave Trough (yt) & Height of The Wave (Hw). 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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