Wavelength for maximum wave steepness Calculator

✖Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [d]			+10% -10%
✖Wave Steepness is defined as the ratio of wave height H to the wavelength λ.ⓘ Wave Steepness [ε_s]			+10% -10%

✖Wavelength can be defined as the distance between two successive crests or troughs of a wave.ⓘ Wavelength for maximum wave steepness [λ]

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Formula

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Wavelength for maximum wave steepness

Formula

`"λ" = 2*pi*"d"/atanh("ε"_{"s"}/0.142)`

Example

`"26.65621m"=2*pi*"0.91m"/atanh("0.03"/0.142)`

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Wavelength for maximum wave steepness Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wavelength = 2*pi*Water Depth/atanh(Wave Steepness/0.142)
λ = 2*pi*d/atanh(ε_s/0.142)
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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)., tanh(Number)
atanh - The inverse hyperbolic tangent function returns the value whose hyperbolic tangent is a number., atanh(Number)

Variables Used

Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.
Wave Steepness - Wave Steepness is defined as the ratio of wave height H to the wavelength λ.

STEP 1: Convert Input(s) to Base Unit

Water Depth: 0.91 Meter --> 0.91 Meter No Conversion Required
Wave Steepness: 0.03 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ = 2*pi*d/atanh(ε_s/0.142) --> 2*pi*0.91/atanh(0.03/0.142)

Evaluating ... ...

λ = 26.6562107209685

STEP 3: Convert Result to Output's Unit

26.6562107209685 Meter --> No Conversion Required

FINAL ANSWER

26.6562107209685 ≈ 26.65621 Meter <-- Wavelength

(Calculation completed in 00.004 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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NSS College of Engineering (NSSCE), Palakkad

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< 18 Wave Parameters Calculators

Major horizontal semi-axis given wavelength, wave height and water depth

Go Horizontal Semi-axis of Water Particle = (Wave Height/2)*(cosh(2*pi*(Distance above the Bottom)/Wavelength))/sinh(2*pi*Water Depth/Wavelength)

Minor vertical semi-axis given wavelength, wave height and water depth

Go Vertical Semi-Axis = (Wave Height/2)*(sinh(2*pi*(Distance above the Bottom)/Wavelength))/sinh(2*pi*Water Depth/Wavelength)

Eckart's Equation for Wavelength

Go Wavelength = (([g]*Wave Period^2/2*pi)*sqrt(tanh(4*pi^2*Water Depth)/Wave Period^2*[g]))

Water Depth for maximum wave steepness of waves travelling

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

Wavelength for maximum wave steepness

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

Maximum Wave Steepness for Waves Travelling

Go Wave Steepness = 0.142*tanh(2*pi*Water Depth/Wavelength)

Wave Amplitude given Elevation of Water Surface Relative to SWL

Go Wave Amplitude = Elevation of Water Surface/cos(Theta)

Elevation of Water Surface Relative to SWL

Go Elevation of Water Surface = Wave Amplitude*cos(Theta)

Phase Velocity or Wave Celerity given Radian Frequency and Wavenumber

Go Celerity of The Wave = Wave Angular Frequency/Wave Number

Radian Frequency given Wave Celerity

Go Wave Angular Frequency = Celerity of The Wave*Wave Number

Wave Number given Wave Celerity

Go Wave Number = Wave Angular Frequency/Celerity of The Wave

Phase Velocity or Wave Celerity

Go Celerity of The Wave = Wavelength/Wave Period

Angular of Radian Frequency of Wave

Go Wave Angular Frequency = 2*pi/Wave Period

Wave Steepness

Go Wave Steepness = Wave Height/Wavelength

Wave number given wavelength

Go Wave Number = 2*pi/Wavelength

Wave Height given Maximum Wave Steepness Limit by Michell

Go Wave Height = Wavelength*0.142

Wavelength given Maximum Wave Steepness Limit by Michell

Go Wavelength = Wave Height/0.142

Wave Amplitude

Go Wave Amplitude = Wave Height/2

Wavelength for maximum wave steepness Formula

Wavelength = 2*pi*Water Depth/atanh(Wave Steepness/0.142)
λ = 2*pi*d/atanh(ε_s/0.142)

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 maximum wave steepness?

Wavelength for maximum wave steepness calculator uses Wavelength = 2*pi*Water Depth/atanh(Wave Steepness/0.142) to calculate the Wavelength, The Wavelength for maximum wave steepness for Waves Travelling in Depths less than Lo/2 is known as the spatial period of a periodic wave—the distance over which the wave's shape repeats. Wavelength is denoted by λ symbol.

How to calculate Wavelength for maximum wave steepness using this online calculator? To use this online calculator for Wavelength for maximum wave steepness, enter Water Depth (d) & Wave Steepness (ε_s) and hit the calculate button. Here is how the Wavelength for maximum wave steepness calculation can be explained with given input values -> 30.75717 = 2*pi*0.91/atanh(0.03/0.142).

FAQ

What is Wavelength for maximum wave steepness?

The Wavelength for maximum wave steepness for Waves Travelling in Depths less than Lo/2 is known as the spatial period of a periodic wave—the distance over which the wave's shape repeats and is represented as λ = 2*pi*d/atanh(ε_s/0.142) or Wavelength = 2*pi*Water Depth/atanh(Wave Steepness/0.142). Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body & Wave Steepness is defined as the ratio of wave height H to the wavelength λ.

How to calculate Wavelength for maximum wave steepness?

The Wavelength for maximum wave steepness for Waves Travelling in Depths less than Lo/2 is known as the spatial period of a periodic wave—the distance over which the wave's shape repeats is calculated using Wavelength = 2*pi*Water Depth/atanh(Wave Steepness/0.142). To calculate Wavelength for maximum wave steepness, you need Water Depth (d) & Wave Steepness (ε_s). With our tool, you need to enter the respective value for Water Depth & Wave Steepness 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?

In this formula, Wavelength uses Water Depth & Wave Steepness. We can use 2 other way(s) to calculate the same, which is/are as follows -

Wavelength = (([g]*Wave Period^2/2*pi)*sqrt(tanh(4*pi^2*Water Depth)/Wave Period^2*[g]))
Wavelength = Wave Height/0.142

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