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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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 00.020 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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< Wave Parameters Calculators

Phase Velocity or Wave Celerity

LaTeX Go Celerity of the Wave = Wavelength/Wave Period

Angular of Radian Frequency of Wave

LaTeX Go Wave Angular Frequency = 2*pi/Wave Period

Wave number given wavelength

LaTeX Go Wave Number = 2*pi/Wavelength

Wave Amplitude

LaTeX Go Wave Amplitude = Wave Height/2

Wavelength for Maximum Wave Steepness Formula

LaTeX Go

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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