Eckart's Equation for Wavelength Solution

STEP 0: Pre-Calculation Summary
Formula Used
Wavelength = (([g]*Wave Period^2/2*pi)*sqrt(tanh(4*pi^2*Water Depth)/Wave Period^2*[g]))
λ = (([g]*P^2/2*pi)*sqrt(tanh(4*pi^2*d)/P^2*[g]))
This formula uses 2 Constants, 2 Functions, 3 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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)
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)
Variables Used
Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Wave Period - Wave Period is the time between successive peaks or troughs.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body.
STEP 1: Convert Input(s) to Base Unit
Wave Period: 1.03 --> No Conversion Required
Water Depth: 1.05 Meter --> 1.05 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
λ = (([g]*P^2/2*pi)*sqrt(tanh(4*pi^2*d)/P^2*[g])) --> (([g]*1.03^2/2*pi)*sqrt(tanh(4*pi^2*1.05)/1.03^2*[g]))
Evaluating ... ...
λ = 49.6864667882897
STEP 3: Convert Result to Output's Unit
49.6864667882897 Meter --> No Conversion Required
FINAL ANSWER
49.6864667882897 49.68647 Meter <-- Wavelength
(Calculation completed in 00.004 seconds)

Credits

Created by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
Mithila Muthamma PA has created this Calculator and 2000+ more calculators!
Verified by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
Chandana P Dev has verified this Calculator and 1700+ more calculators!

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

Eckart's Equation for Wavelength Formula

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

What are Water waves ?

Wave, a ridge or swell on the surface of a body of water, normally having a forward motion distinct from the oscillatory motion of the particles that successively compose it. Water waves are considered oscillatory or nearly oscillatory if the motion described by the water particles is circular orbits that are closed or nearly closed for each wave period.

How to Calculate Eckart's Equation for Wavelength?

Eckart's Equation for Wavelength calculator uses Wavelength = (([g]*Wave Period^2/2*pi)*sqrt(tanh(4*pi^2*Water Depth)/Wave Period^2*[g])) to calculate the Wavelength, The Eckart's Equation for Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space. Wavelength is denoted by λ symbol.

How to calculate Eckart's Equation for Wavelength using this online calculator? To use this online calculator for Eckart's Equation for Wavelength, enter Wave Period (P) & Water Depth (d) and hit the calculate button. Here is how the Eckart's Equation for Wavelength calculation can be explained with given input values -> 49.68647 = (([g]*1.03^2/2*pi)*sqrt(tanh(4*pi^2*1.05)/1.03^2*[g])).

FAQ

What is Eckart's Equation for Wavelength?
The Eckart's Equation for Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space and is represented as λ = (([g]*P^2/2*pi)*sqrt(tanh(4*pi^2*d)/P^2*[g])) or Wavelength = (([g]*Wave Period^2/2*pi)*sqrt(tanh(4*pi^2*Water Depth)/Wave Period^2*[g])). Wave Period is the time between successive peaks or troughs & Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body.
How to calculate Eckart's Equation for Wavelength?
The Eckart's Equation for Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space is calculated using Wavelength = (([g]*Wave Period^2/2*pi)*sqrt(tanh(4*pi^2*Water Depth)/Wave Period^2*[g])). To calculate Eckart's Equation for Wavelength, you need Wave Period (P) & Water Depth (d). With our tool, you need to enter the respective value for Wave Period & Water Depth 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 Wave Period & Water Depth. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Wavelength = Wave Height/0.142
  • Wavelength = 2*pi*Water Depth/atanh(Wave Steepness/0.142)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!