Wavelength as Function of Water Depth and Wave Period Solution

STEP 0: Pre-Calculation Summary
Formula Used
Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth)
λ = (([g]*T)/ω)*tanh(k*d)
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
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)
Variables Used
Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Wave Period - (Measured in Second) - Wave Period is the time between successive peaks or troughs.
Wave Angular Frequency - (Measured in Radian per Second) - Wave Angular Frequency angular displacement of the wave per unit time. Its units are therefore degrees (or radians) per second.
Wave Number - The wave number quantifies the number of waves per unit length along the surface of the water.
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: 3 Second --> 3 Second No Conversion Required
Wave Angular Frequency: 2.5 Radian per Second --> 2.5 Radian per Second No Conversion Required
Wave Number: 5 --> No Conversion Required
Water Depth: 1.55 Meter --> 1.55 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
λ = (([g]*T)/ω)*tanh(k*d) --> (([g]*3)/2.5)*tanh(5*1.55)
Evaluating ... ...
λ = 11.7679756331591
STEP 3: Convert Result to Output's Unit
11.7679756331591 Meter --> No Conversion Required
FINAL ANSWER
11.7679756331591 11.76798 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
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14 Wavelength Calculators

Water depth given wave celerity and wavelength
Go Water Depth = (Wavelength*atanh((2*pi*Wave Celerity)/([g]*Wave Period)))/(2*pi)
Wavelength given wave celerity and wave speed
Go Wavelength = (2*pi*Water Depth)/(atanh((2*Wave Celerity*pi)/([g]*Wave Period)))
Eckert's equation for Wavelength
Go Wavelength = Deep-Water Wavelength*sqrt(tanh((2*pi*Water Depth)/Deep-Water Wavelength))
Wavelength as Function of Water Depth and Wave Period
Go Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth)
Wavelength as Function of Depth and Wave Period
Go Wavelength = (([g]*Wave Period^2)/(2*pi))*tanh(Wave Number*Water Depth)
Wavelength given Deepwater Wavelength
Go Wavelength = Deep-Water Wavelength*tanh(Wave Number*Water Depth)
Long Wave simplification for Wavelength
Go Wavelength = Wave Period*sqrt([g]*Water Depth)
Wavelength given Deepwater celerity and Deepwater wavelength
Go Wavelength = (Deep-Water Wavelength*Wave Celerity)/Deepwater Wave Celerity
Deepwater wavelength given Deepwater celerity
Go Deep-Water Wavelength = (Wavelength*Deepwater Wave Celerity)/Wave Celerity
Deepwater Wavelength given Celerity of Deepwater Wave
Go Deep-Water Wavelength = (Deepwater Wave Celerity^2*2*pi)/[g]
Deepwater Wavelength given Wave Celerity
Go Deep-Water Wavelength = Deepwater Wave Celerity*Wave Period
Wavelength given wave celerity
Go Wavelength = Wave Celerity*Wave Period
Deepwater Wavelength given Units of Feet
Go Deep-Water Wavelength in Feet = 5.12*Wave Period^2
Deepwater Wavelength when SI systems Units of meters is considered
Go Deep-Water Wavelength = 1.56*Wave Period^2

Wavelength as Function of Water Depth and Wave Period Formula

Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth)
λ = (([g]*T)/ω)*tanh(k*d)

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 Wavelength as Function of Water Depth and Wave Period?

Wavelength as Function of Water Depth and Wave Period calculator uses Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth) to calculate the Wavelength, The Wavelength as Function of Water Depth and Wave Period is distance between identical points (adjacent crests) in adjacent cycles of waveform signal propagated in space. Wavelength is denoted by λ symbol.

How to calculate Wavelength as Function of Water Depth and Wave Period using this online calculator? To use this online calculator for Wavelength as Function of Water Depth and Wave Period, enter Wave Period (T), Wave Angular Frequency (ω), Wave Number (k) & Water Depth (d) and hit the calculate button. Here is how the Wavelength as Function of Water Depth and Wave Period calculation can be explained with given input values -> 11.76733 = (([g]*3)/2.5)*tanh(5*1.55).

FAQ

What is Wavelength as Function of Water Depth and Wave Period?
The Wavelength as Function of Water Depth and Wave Period is distance between identical points (adjacent crests) in adjacent cycles of waveform signal propagated in space and is represented as λ = (([g]*T)/ω)*tanh(k*d) or Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth). Wave Period is the time between successive peaks or troughs, Wave Angular Frequency angular displacement of the wave per unit time. Its units are therefore degrees (or radians) per second, The wave number quantifies the number of waves per unit length along the surface of the water & 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 Wavelength as Function of Water Depth and Wave Period?
The Wavelength as Function of Water Depth and Wave Period is distance between identical points (adjacent crests) in adjacent cycles of waveform signal propagated in space is calculated using Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth). To calculate Wavelength as Function of Water Depth and Wave Period, you need Wave Period (T), Wave Angular Frequency (ω), Wave Number (k) & Water Depth (d). With our tool, you need to enter the respective value for Wave Period, Wave Angular Frequency, Wave Number & 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, Wave Angular Frequency, Wave Number & Water Depth. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Wavelength = Wave Celerity*Wave Period
  • Wavelength = (2*pi*Water Depth)/(atanh((2*Wave Celerity*pi)/([g]*Wave Period)))
  • Wavelength = (([g]*Wave Period^2)/(2*pi))*tanh(Wave Number*Water Depth)
  • Wavelength = (Deep-Water Wavelength*Wave Celerity)/Deepwater Wave Celerity
  • Wavelength = Deep-Water Wavelength*tanh(Wave Number*Water Depth)
  • Wavelength = Deep-Water Wavelength*sqrt(tanh((2*pi*Water Depth)/Deep-Water Wavelength))
  • Wavelength = Wave Period*sqrt([g]*Water Depth)
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